Numerical simulation of the problem arising - ECMI 2004

Transcription

The 13th European Conference
on Mathematics in Industry
June 21–25, 2004
Eindhoven, The Netherlands
Organized by:
Technische Universiteit Eindhoven
European Consortium for Mathematics in Industry
European Network for Business and Industrial Statistics
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Colofon
• design cover: Peter Peels
• composition and editing: Alessandro Di Bucchianico, Paul de Haas,
Mark Peletier
• printing: Printservice TU/e
Programme Committee
The Board of ECMI
R. Caflisch (Los Angeles)
M. Davies (London)
A. Friedman (Columbus, OH)
A. Frigessi (Oslo)
T. Gimse (SINTEF, Oslo)
P. Landrock (Aarhus)
R. Mattheij (Eindhoven)
E. Oñate (Barcelona)
J. Periaux (Dassault, Paris)
O. Pironneau (Paris)
M. Primicerio (Firenze)
W. Schilders (Philips, Eindhoven)
K. Sigmund (Vienna)
H. Holden (Trondheim)
L. Bonilla (Madrid)
H. Ockendon (Oxford)
A. Neubauer (Linz)
The Board of ENBIS/PRO-ENBIS
T. Greenfield (Weyhill)
P. Thyregod (Kongens Lungby)
D. Stewardson (Newcastle)
Local Scientific Committee
H. van Duijn
P. Hilbers
H. Hoeijmakers
J. Molenaar
W. Schilders
H. Schumacher
J. Teugels
H. van Tilborg
J. van de Vegt
F. van de Vosse
G. de With
Local Organising Committee
A. Di Bucchianico
C. Damsma
E. van Dijk
P. de Haas
H. Horvath
J. Houtsmuller
M. Peletier
R. Mattheij
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Contents
1
Welcome
1.1 About ECMI . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 About ENBIS and Pro-ENBIS . . . . . . . . . . . . . . . .
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General information
2.1 Location . . . . . . . . . . . . . . . .
2.2 Conference desk . . . . . . . . . . . .
2.3 Information for the speakers . . . . .
2.4 Information about the poster sessions .
2.5 Exhibition . . . . . . . . . . . . . . .
2.6 Internet café . . . . . . . . . . . . . .
2.7 Lunches . . . . . . . . . . . . . . . .
2.8 Coffee and tea breaks . . . . . . . . .
2.9 Proceedings . . . . . . . . . . . . . .
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Programme overview
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Social events
4.1 Welcome reception
4.2 Excursion . . . . .
4.3 Conference dinner .
4.4 Concert . . . . . .
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Sponsors
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Abstracts of presentations and posters
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Index
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Maps of the Auditorium
264
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Welcome
1
Welcome
Dear Conference participant,
In the autumn of 1985 ESMI (European Symposium on Mathematics in
Industry), the predecessor of ECMI, took place in Amsterdam. During that
meeting the ideas were born that eventually lead to the foundation of ECMI as
we know it now. Many successful meetings followed this ECMI-0, but it took
nearly 20 years to have another one held in the Netherlands again. A significant number of participants who were present at ESMI are also here and they
will undoubtedly agree with me that the adulthood of ECMI is apparent from
the many things it has achieved since then. ECMI has become a brandname
for industrial mathematics. We are proud therefore to be your host this year.
TU/e is a relatively young university. Also the city of Eindhoven looks rather
young, despite the fact that it has an old history. This modern face of the city
is probably typical for the spirit here and, for that matter, in the larger region.
Greater Eindhoven ranks among the top three in European technological and
industrial innovation. The theme of this conference, industrial mathematics,
is nicely fitting in with this. Indeed, nowadays mathematics is generally accepted as a technology, playing a crucial role in many branches of industrial
activity, for optimising both processes and products.
We are happy that so many people have shown their interest in this conference. We have more than 320 talks and about 400 participants, from all
continents. The large numbers imply that we have many parallel sessions.
We have taken care though to schedule the talks and minisymposia in such a
way that thematically similar topics do not overlap.
Apart from the scientific programme we have some nice social events.
They have been made possible, partly thanks to generous sponsoring by institutional and industrial companies. Their support is a double pleasure as
it also signifies their interest in industrial mathematics per se. We therefore
cordially invite you to participate in the reception by the Mayor of Eindhoven
on Monday night, the excursion to the Hoge Veluwe on Wednesday, the conference dinner that night and the concert on Thursday evening. All events are
free for the participants of this meeting.
Organizing a meeting like this is a multi-person undertaking. During these
last two and a half years this event has been prepared by a dedicated group
of people, this week eventually growing to quite a large number of persons
who will be actively involved in the lubrication of it all. We are very grateful
for their help. Also the dedication of our university congress bureau makes
us trust ECMI2004 to be rather speckless. It goes without saying, however,
that the actual success of this meeting for you crucially depends on your own
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Welcome
active participation. On behalf of the organising committee it is therefore my
pleasure to wish you an interesting, fruitful and, most of all, enjoyable conference.
Bob Mattheij
1.1
About ECMI
The development of high speed computers and the ever increasing use of
advanced mathematical models in almost every aspect of our modern technological society, has changed the way mathematician work in industry. The
development requires better mathematical methods, and an interesting aspect
is that this is a two-way street: Applications provide challenging questions,
and theoretical insight improves solutions.
The European Consortium for Mathematics in Industry (ECMI) was
founded in 1986 by mathematicians from ten European universities to address the question of how to prepare young European mathematicians for an
active career in industrial mathematics.
The aims of ECMI are
• To promote the use of mathematical models in industry.
• To educate industrial mathematicians to meet the growing demand for
such experts.
• To operate on a European scale.
ECMI has an institutional, industrial and individual membership. While
continuing to train industrial mathematicians it is also engaged in a variety
of research collaborations and networking activities. Information is given via
the Newsletters and the web page www.ecmi.dk.
One of the major projects that ECMI is involved in is MACSI-net.
MACSI-net (MAthematics Computing and Simulation for Industry) is a
EU-funded network of excellence, which among other things has produced
the road map ‘MATHEMATICS, Key to the European Knowledge-based
Economy’. For more information on MACSI-net please consult www.
macsinet.org.
1.2
About ENBIS and Pro-ENBIS
Many applied statisticians and statistical practitioners work in professional
environments where they are rather isolated from interactions and stimula6
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Welcome
tion from like-minded professionals. Statistics is vital for the economic and
technical development and improved competitiveness of European industry.
To this end the European Network for Business and Industrial Statistics (ENBIS) was founded in 2000.
The mission of ENBIS is to
• foster and facilitate the application and understanding of statistical
methods to the benefit of European business and industry,
• provide a forum for the dynamic exchange of ideas and facilitate networking among statistical practitioners (a statistical practitioner is any
person using statistical methods whether formally trained or not), and
• nurture interactions and professional development of statistical practitioners regionally and internationally.
ENBIS is a web based society (www.enbis.org):
• Membership interactions and administration are done via the internet;
• Services, news, and newsletter are available on the web.
Pro-ENBIS is a thematic network contracted for three years (2001-2004)
by the European Commission. The Pro-ENBIS project is supported by
funding under the European Commission’s Fifth Framework ’Growth’ Programme.
For more information, please consult the web page of Pro-ENBIS at
www.enbis.org/pro-enbis/.
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2.1
General information
General information
Location
Almost all activities of the conference take place in the Auditorium of the
Technische Universiteit Eindhoven. Signs indicate the way to the entrances.
On the map below the Auditorium is indicated as building AUD. Maps of the
Auditorium itself are shown on the last page of this book.
The welcome reception, the excursion and the conference dinner are not
on the campus of the university. These activities and how to get there are
described separately in section 4 on social events.
TU/e campus
Auditorium
Railway station
See also the map of the center of Eindhoven on page 12.
2.2
Conference desk
Details of your registration can be discussed at the conference desk on floor 1
of the Auditorium. Information about your hotel reservation (if the reservation has been made by the congress office) also is available here. The conference desk telephone number is 040-2474000.
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General information
2.3
Information for the speakers
• There will be a person available in each lecture hall before (30 minutes)
and during each session to assist you in technical matters.
• If you have a Powerpoint or PDF presentation, please make sure to
test it well in advance. You may connect your own laptop, but the
transition between presentations will be quicker if you transfer the file
to the standard laptop in the room. The technical assistant in the room
can do this for you.
• Please avoid delays between talks and be on time as indicated in the
schedule. It will be appreciated by everyone if you finish on time as
well so that switching between sessions may be smooth.
• Please fill in your brief CV (you can find a form in the conference bag)
and hand it over to the chairman of your session before you speak. This
will facilitate him/her introducing you.
2.4
Information about the poster sessions
Tuesday and Thursday are devoted to the presentation of the posters. In the
main hall of the auditorium ample space will be available. Poster presenters
are asked to accompany their posters during the breaks. The organization will
assist in hanging the posters 15 minutes before the start of the morning and
afternoon sessions on the poster panels. Please report to the conference desk
before hanging the poster.
2.5
Exhibition
There will be exhibitions by book publishers, software vendors and industrial
companies. These will be set up in the main hall of the auditorium where
participants of the conference will gather between sessions.
2.6
Internet café
In Hall 9 you can use one of the laptops to connect to the internet and check
your mailbox, find some on-line information or download missing files (floppies not provided).
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2.7
General information
Lunches
Lunch is served in the Senaatszaal, see the maps of the Auditorium on
page 264.
2.8
Coffee and tea breaks
Coffee and tea are served in the main hall, near the exhibition.
2.9
Proceedings
There will be refereed conference proceedings, to be published by Springer
Verlag. The ECMI 2004 proceedings will be produced using special LATEX
style files from Springer. Please visit the ECMI 2004 website at
http://www.ecmi2004.tue.nl
for specific instructions how to format and submit your files. The deadline
for submission is September 17, 2004.
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Programme overview
Sunday
Tuesday
07.30
09.00
09.30
10.30
11.00
09.00
10.00
10.30
13.00 Lunch
14.00 J. Hinch
15.00 Break
15.30–17.30 MS + CP
evening
afternoon
morning
evening
Monday
morning
Programme overview
afternoon
3
18.00–20.00
Registration
Registration
Opening
B. Schrefler
Break
MS + CP
B. Trowbridge
Break
MS + CP
12.30 Lunch
13.30 S. Bisgaard
14.30 F. Ruggeri
15.30 Break
16.00–18.00 MS + CP
19.00–21.00 Welcome
reception in the
Daf museum
Wednesday
Thursday
Friday
09.00
10.00
10.30
09.00 R. Helmig
10.00 Break
10.30 MS + CP
08.30
09.30
10.00
M. Waterman
Break
MS + CP
12.30 Excursion to
Kröller-Müller
museum
(lunch included)
12.30 Lunch
13.30 J. Hunt
14.30 Break
15.00-17.00
MS + CP
12.00
13.00
14.00
14.15
16.15
16.45
Lunch
C. Rossow
Break
MS + CP
Wacker lecture
Closing
19.00–23.00
Conference dinner
in Evoluon
20.15–22.00
Helikon orchestra
L. C. G. Rogers
Break
MS + CP
MS + CP: Minisymposia and sessions of contributed presentations
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4.1
Social events
Social events
Welcome reception
Monday June 21, 19.00-21.00
The welcome reception will be in the DAF Museum and is offered by the
mayor of Eindhoven, mr. A.B. Sakkers. The museum is devoted to the Dutch
automobile industry and to DAF in particular.
The DAF Museum is on 20 minutes walking distance of both campus and
railway station. See the map below for directions. The address is Tongelresestraat 27, 5613 DA Eindhoven, tel.: 040-2444264.
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Social events
4.2
Excursion
Wednesday June 23, 12.30-19.00
Directly after the Wednesday morning session there will be an excursion
to the Kröller-Müller museum. Lunch will be served during the excursion.
You will be taken to the museum by bus (1.5 hrs drive) leaving from the Auditorium. On return the buses will take you to the Evoluon for the conference
dinner, or if you do not join the conference dinner, back to the Auditorium.
The Kröller-Müller museum houses a world famous collection of fine art,
mainly from the 19th and 20th centuries. The focal points of the museum are
the extensive range of works by Vincent van Gogh and the sculpture garden.
The Kröller-Müller museum and the Hoge Veluwe National Park, the legacy
of Mr and Mrs Kröller-Müller, form a monumental ensemble of art, architecture and nature. For more than seventy years this unique combination has
attracted vast numbers of art and nature lovers from all over the world to the
Veluwe.
4.3
Conference dinner
Wednesday June 23, 19.00-23.00
The conference dinner will be in the Evoluon. If you join the excursion
you will be dropped off at the Evoluon at 19.00 hrs. If you do not join the
excursion you can make use of the buses which leave at 19.30 hrs (the latest)
from the Auditorium. After the conference dinner the buses will stop at the
conference hotels.
You can also go by yourself by taxi or by bus (leaving from the central
station - lines 401, 16 or 17).
Address:
Noord Brabantlaan 1A
5652 LA Eindhoven
Tel.: 040-2504666
4.4
Concert
Thursday June 24, 20.15-22.00
Location: Blauwe Zaal, Auditorium Technische Universiteit Eindhoven
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Social events
The Eindhovense Orkestvereniging Helikon, usually called the Helikon
orchestra, is a symphony orchestra consisting of around 75 amateur musicians, some of them with a (semi-)professional background. The orchestra
was started on December 11, 1969 with the merger of the ‘The small symphony orchestra’ and the former student orchestra of the University in Eindhoven, at that time still called Technische Hogeschool. The name Helikon
(mountain of the muses) originates from the so called Helikon hall from the
Philips Ontspanningscentrum (POC), where the orchestra used to rehearse.
From the start until 2001, Jacques Wijnen was the principal conductor of the
Helikon orchestra.
The present conductor, Kian Pin Hiu, who grew up in China, played first
violin for 25 years in the Royal Concertgebouworchestra in Amsterdam. After his retirement from this orchestra he has devoted himself completely to
conducting. His expertise is based on his rich experience with world famous conductors and solo performers, his inspiring charisma and the ability
to create a homogenous group from musically different characters. During
his four-year tenure as conductor, he has brought the Helikon orchestra to a
completely different level, as is testified by the press reviews from concerts
during the period.
Helikon has a wide repertoire largely from the classical and romantic periods which includes works such as the 2nd symphony from Sibelius, the
4th and 5th symphonies of Tsjaikovsky, the 1st and 5th symphonies from
Beethoven and various concertos with international solo performers such as
Mendelssohn’s concerto for violin in E with Alexander Kerr and Dvorak’s
concerto for cello in B sharp with Godfried Hoogeveen. In the traditional autumn concert in November, the Helikon orchestra will play Beethoven’s 9th
symphony and Haydn’s symphony ‘The Clock’.
The programme of the concert played at ECMI 2004 will be lighter. In
the first half the orchestra will play Mozart’s Linzer symphony and the Petite
Symphony by Gounod for wind players. After the break the Farendole from
Bizet’s Arlesienne suite will be played and Bizet’s Carmen Suite. The concert
will close with Fuçik’s Florentiner Marsch.
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Sponsors
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Sponsors
We are very grateful for the support of our sponsors:
ABN AMRO
www.abnamro.com
Beta
www.tm.tue.nl/beta
Cambridge University Press
uk.cambridge.org
CANdiensten
www.candiensten.nl
Dow Chemical
www.dow.com
Eldim
www.eldim.nl
Engineering Mechanics
www.wfw.wtb.tue.nl/em
EURANDOM
www.eurandom.nl
Gemeente Eindhoven
www.eindhoven.nl
J.M. Burgerscentrum
www.burgerscentrum.org
IBIS UvA BV
www.ibisuva.nl
KNAW
www.knaw.nl
MATTeR research school
MRI
www-mri.sci.kun.nl
NWO
www.nwo.nl
R. Timman Stichting
Océ
www.oce.com
Philips Medical Systems
www.medical.philips.com
Philips Research
www.research.philips.com
Shell
www.shell.com
Sodexho
www.sodexho.nl
Springer Verlag
www.springer.de
Thomas Stieltjes Institute for Mathematics
www.math.leidenuniv.nl/˜stieltjes
Thales
www.thalesgroup.com
TNO
www.tno.nl
ttec/transtec
www.transtec.de
WL|Delft Hydraulics
www.wldelft.nl
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Sponsors
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Abstracts
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Abstracts
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Monday Morning
Monday Morning
9:30–10:30
Plenary lecture
A multiphase model for concrete: numerical solutions and industrial applications (B. Schrefler) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10:30–11:00
Break
11:00–13:00
Minisymposia and contributed presentations
Application of Model Order Reduction methods in an industrial environment (P.J. Heres; theme: Electronic industry) . . . . . . . . . . . . . . .
An accurate and compact modeling algorithm for deterministic LTI systems,
based on multiprecision arithmetic (D. Deschrijver) . . . . . . . . . . . .
Model Order Reduction of non-linear dynamical systems (R. Ivanov) . . . .
Krylov subspace methods in the electronic industry (P.J. Heres) . . . . . . .
Vector Fitting from a mathematical point of view (W. Hendrickx) . . . . . .
Multiscale methods for flow in porous media (K.-A. Lie; theme: Geophysics)
Two-Phase Flow Simulation by AMMoC, an Adaptive Meshfree Method of
Characteristics (A. Iske) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiscale methods and streamline simulation for rapid reservoir performance prediction (K.-A. Lie) . . . . . . . . . . . . . . . . . . . . . . . .
Multi-Scale Finite-Volume Method for Multi-Phase Flow in Highly Heterogeneous Reservoirs (P. Jenny) . . . . . . . . . . . . . . . . . . . . . . . .
Stable and accurate simulation of multiphase flow in porous media through
separation of scales (R. Juanes) . . . . . . . . . . . . . . . . . . . . . . .
Dynamic Capillary Pressure Effects in Multi-Phase Flow in Porous Media
(I.S. Pop) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Non-classical travelling waves for Buckley-Leverett via a pseudo-parabolic
degenerate regularisation. (C.M. Cuesta) . . . . . . . . . . . . . . . . . .
A new class of entropy solutions of the Buckley - Leverett equation (C.J. van
Duijn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dynamic effect in capillary pressure-saturation relationships in unsaturated
media and two-phase flow(S. Majid Hassanizadeh) . . . . . . . . . . . . .
Modern Industrial Statistics in the Industry (E.M. Jordaan) . . . . . . . . .
The application of reliability simulation in the process industry. (R.M. Dauwe)
Multivariate analysis of sensory coffee data. (G.D. Mooiweer) . . . . . . . .
Robust design using computer experiments (R.S. Kenett) . . . . . . . . . . .
Model and Similarity-based Methods for the Recognition of Fungi Spores in
Images (P. Perner) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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BZ
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H 11
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23 H 13
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H5
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29 H 7
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Monday Morning
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Examples of ECMI graduate student projects (M.P. Sørensen) . . . . . . .
Optimal Prediction in Molecular Dynamics (B. Seibold) . . . . . . . . . . .
Rattle in geared systems (C.K. Halse) . . . . . . . . . . . . . . . . . . . . .
Dynamics of a Helicopter Lag Damper (R.D. Eyres) . . . . . . . . . . . . .
Near-Earth Objects: Theory, Detection and Observation (S. Wolff) . . . . . .
Contributed presentations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Imaging Convex Inclusions in Uniform Conductors based on Electrical
Boundary Measurements (D. Roy) . . . . . . . . . . . . . . . . . . . . .
Sound Scattering by a Spherical Object Near an Impedance Plane (M. Seyyed)
Periodic Optimal Control Applications in Chemical Engineering (M. Diehl) .
A Goodness of Fit Test For Linear Hypothesis In Nonparametric Regression
Model (Z. Mohdeb) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistical thermodynamics for choice models on graphs. (A. Majka) . . . .
Multi-Threaded Application of Monothetic Clustering Method (G. Brunet) .
31 H 4
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33 H 14
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A multiphase model for concrete: numerical solutions and industrial
applications
B. Schrefler (University of Padova), D. Gawin (Technical University of
Lodz), F. Pesavento (University of Padova)
Monday, 9:30–10:30, Blauwe Zaal
In several situations it is necessary to model concrete as a multiphase material, i.e. a material made up of a solid phase and pores which are filled
with different fluid phases. Typical cases deal with concrete performance in
the high temperature range, e.g. during fire, with early stages of maturing of
massive concrete structures, with shotcrete in tunnelling, and with durability.
We present here a general model for chemo-hygro-thermo-mechanical analysis of concrete applicable to the above situations. Moist concrete is modelled
as a multi-phase material, which is assumed to be in thermo-dynamic equilibrium state locally. The voids of the skeleton are filled partly with liquid
water and partly with a gas phase. The liquid phase consists of bound water,
which is present in the whole range of moisture content, and capillary water,
which appears when water content exceeds the upper limit of the hygroscopic
region, Sssp . The gas phase is a mixture of dry air and water vapour, and is
assumed to be an ideal gas. The chosen primary variables of the model are:
gas pressure p g , capillary pressure p c = p g − p w ( p w denotes water pressure), temperature T , displacement vector of the solid matrix u, as well as
degree of cement hydration 0hydr , when hydration or dehydration phenomena
20
Monday Morning
are analysed, or carbon dioxide concentration ρ d and degree of carbonation
0carb , when carbonation is considered. All the important phase changes of
water, i.e. adsorption-desorption, condensation-evaporation, and chemical reactions, e.g. hydration-dehydration carbonation/decarbonation, as well as the
related heat and mass sources (or sinks) are considered. Changes of the material properties caused by temperature and pressure changes, concrete damage,
fresh concrete hardening, aging process and creep, as well as couplings between thermal, hygral, chemical and mechanical phenomena are taken into
account. This model further allows to incorporate sorption hysteresis.
Minisymposium: Application of Model Order Reduction methods in an
industrial environment
P.J. Heres (Technische Universiteit Eindhoven), W.H.A. Schilders (Philips
Research Laboratory)
Monday, 11:00–13:00, Hall 11
In many industrial simulation tools, nowadays there is a growing demand
to dynamically couple two methodologically different computational models
with each other. This is a computationally demanding task and therefore not
always feasible. To make this coupling numerically more attractive one often tries to capture the essential physical behavior of a model into a more
compact computational model. Over the last few decades a wide range of
mathematical methods have been developed to reduce the order of a model.
These Model Order Reduction methods replace a large model by a much
smaller behavioral model, while preserving essential features of the model,
like for instance stability. Many of these methods have a strong relation with
mathematical methods in numerical linear algebra and system theory. To ensure accuracy and efficiency in the implementation of the methods, one needs
a thorough mathematical knowledge, which makes the whole a challenging
subject. In this mini-symposium we would like to give an overview of the
reduction methods which are possibly applicable in an industrial context. Especially in the electronic industry Model Order Reduction methods have been
implemented and validated successfully, in this session a more detailed view
on this side of applications will be given.
Monday Morning
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An accurate and compact modeling algorithm for deterministic LTI systems, based on multiprecision arithmetic
D. Deschrijver (University of Antwerp), W. Hendrickx (University of
Antwerp), T. Dhaene (University of Antwerp), F. Arickx (University of
Antwerp)
Monday, 11:00–11:30, Hall 11
Linear Time Invariant (LTI) systems can be modeled in the frequency domain
by rational pole-zero models. Least squares approximation techniques are often used to calculate the coefficients of the rational functions. Usually, this
involves the inversion of a Vandermonde-like system of equations, which is
notoriously ill-conditioned. Some of the numerical issues can be resolved
by expanding the numerator and denominator polynomial into a Chebyshev
or Forsythe orthogonal basis. But this approach still fails to model highly
dynamic systems (i.e., systems with a large number of poles). Rational interpolation techniques such as Thiele-type branched continued fractions or
recursive interpolation algorithms, combined with an adaptive sampling strategy, are numerically more efficient, but these methods cannot impose physical
constraints such as causality and passivity. In this paper, numerical accuracy
issues are resolved by fitting the models in a multi-precision floating-point
arithmetic environment, which combines most advantages of the techniques
mentioned above and avoids the use of multiple splines.
Model Order Reduction of non-linear dynamical systems
R. Ivanov (Dublin City University), C. Brennan (Dublin City University),
M. Condon (Dublin City University)
Monday, 11:30–12:00, Hall 11
The talk is concerned with model reduction of nonlinear systems. Such systems arise in all aspects of engineering - aeronautics, chemical and processing industries, high-speed electronics and so on. Be it in the design of the
systems themselves or in the design of controllers for these systems, simple
models that capture the essential behaviour of the systems are crucial. However, the complexity of modern systems is such that their simulation may
involve the solution of several thousands of non-linear ordinary or partial differential equations. This can prove computationally arduous both in terms
of speed and memory requirements even with state-of-the-art workstations.
To this end, model reduction techniques are of paramount importance in that
they permit repetitive simulation for both design and optimisation purposes to
proceed in a reasonable time-frame. Now while model reduction techniques
for linear systems abound, nonlinear model reduction is in its infancy and a
general user-friendly robust technique remains to be found. One approach
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for linear reduction familiar to engineers is balanced truncation. It involves
the determination of two specific matrices, ‘gramians’, which when balanced
enable the important states in a system to be determined and those of lesser
importance to be eliminated. For nonlinear systems, the computation of exact
gramians is impractical so empirical gramians are required in lieu of the exact
solutions. This enables a balancing type model reduction process to proceed
for nonlinear systems in the same manner as for linear systems. The talk
will discuss several novel approaches for the determination of approximate
gramians and the relative merits of each. Several practical examples will be
given to indicate their efficacy. The generality and widespread applicability
of the approaches in all branches of industry will be emphasised throughout
the talk.
Krylov subspace methods in the electronic industry
P.J. Heres (Technische Universiteit Eindhoven)
Monday, 12:00–12:30, Hall 11
Model Order Reduction tries to replace a large model by a computationally
smaller model. Recently Model Order Reduction has gained a lot of interest in industry. Also a large variety of methods is developed in the last few
decades. One very interesting class of methods is the Krylov subspace methods. These methods are interesting because they are generally applicable
and relatively cheap and can therefore be applied to relatively large systems,
which makes them suitable for an industrial context.
The methods are applied on time invariant linear DAE system of the following
form:
C
d
x(t) + Gx(t) =
dt
y =
Bu(t)
L T x(t),
where u(t) is an input function, x(t) the state space of the system and y(t)
the output. A Krylov subspace method generates a Krylov space associated
with the input matrix B: Kq (B, A) = [B, AB, A2 B, . . . , Aq B]. The system
matrices C and G are projected on a small orthogonal basis of the Krylov
space.
In this talk we will explain the different approaches proposed in the several
methods of this class. But more important are the practical issues one encounters when implementing this method. Mathematical knowledge is needed to
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make the methods suitable for an industrial context. Especially the orthogonalisation of the Krylov space will have our attention. On the one hand careful
implementation of orthogonalisation is needed to avoid errors. On the other
hand orthogonalisation can be exploited to improve the methods. Finally, we
will show an example of the application of Model Order Reduction methods
in an EM simulator, a tool used in the electronic industry.
Vector Fitting from a mathematical point of view
W. Hendrickx (University of Antwerp), T. Dhaene (University of Antwerp),
F. Arickx (University of Antwerp)
Monday, 12:30–13:00, Hall 11
Rational approximation plays a crucial role in the theory of Linear TimeInvariant (LTI) systems. Unfortunately, finding such an approximation leads
to several mathematical subtleties. Especially in least-squares rational approximation we need to solve systems of non-linear equations. To overcome
this problem, it’s commonplace to fix the denominator at a certain polynomial
or to linearize the system in some other way. In most cases, the resulting approximation will be inferior to the true least-squares solution of the system,
due to the introduction of unbalanced weighting.
In the late 90’s, Gustavsen and Semlyen introduced the Vector Fitting
(VF) technique in Power System engineering. Using the VF approach they
achieved highly accurate rational models of measured frequency domain data.
VF iteratively generates more accurate estimations of the poles of the rational approximation. So far, VF has only been used from a practitioners point
of view, and not much theory exists to back-up the VF methodology. In this
paper we try to elaborate the mathematics behind Vector Fitting and to place
the scheme in the broader context of rational least-squares approximation.
Minisymposium: Multiscale methods for flow in porous media
K.-A. Lie (SINTEF IKT), J E Aarnes (SINTEF IKT)
Monday, 11:00–13:00, Hall 13
Oil and gas companies depend on computer simulation of reservoir flow scenarios to plan and manage production from their hydrocarbon reserves. Natural porous formations are heterogeneous at all length scales. Small-scale
heterogeneities can significantly affect large-scale fluid transport. To accurately resolve these heterogeneities, stochastic reservoir characterization
models may contain 108 grid blocks or more. Current reservoir simulators
are limited to 105 − 106 grid blocks. One therefore uses upscaling to reduced
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the set of parameters and generate coarser grids as simulator input. To date,
no upscaling regime has been shown to perform well for the whole range of
flow scenarios encountered in real reservoirs. Moreover, upscaling lacks a
rigorous mathematical foundation.
Multiscale methods may prove to be a good alternative to upscaling. These
methods reduce the computational complexity by incorporating fine-scale
features into a set of coarse grid equations that are consistent with the local
property of the differential operator.
This minisymposium will address the use of multi-scale methods to enhance our understanding of flow processes in heterogeneous porous media
and show how the reduced computational complexity can offer new insight
into the impact of the fine scale features.
Two-Phase Flow Simulation by AMMoC, an Adaptive Meshfree Method
of Characteristics
A. Iske (Technische Universität München), Martin Käser (Technische Universität München)
Monday, 11:00–11:30, Hall 13
Petroleum reservoir modelling requires effective multiscale methods for the
numerical simulation of two-phase flow in porous media. This talk proposes a
novel meshfree particle method for the Buckley-Leverett model. The utilized
meshfree advection scheme, called AMMoC, is essentially a method of backward characteristics, which combines an adaptive semi-Lagrangian method
with local meshfree interpolation by polyharmonic splines. The method AMMoC is applied to the five-spot problem, a well-established model problem
in petroleum reservoir simulation. The numerical results and subsequent
numerical comparisons with two leading commercial reservoir simulators,
ECLIPSE and FrontSim of Schlumberger, show the good performance of our
meshfree advection scheme AMMoC.
Multiscale methods and streamline simulation for rapid reservoir performance prediction
K.-A. Lie (SINTEF IKT), V. Kippe (SINTEF IKT)
Monday, 11:30–12:00, Hall 13
Streamline methods are gaining in popularity and provide desktop simulation of large reservoir models. Traditionally, streamline simulators have been
based upon simplified physics, but recent advances have demonstrated the
potential for more complex physics like compressible three-phase or component models. Streamline methods are based upon a fractional flow formula-
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tion, where the model is split into an elliptic/parabolic pressure equation and
hyperbolic fluid transport equations.
A major obstacle in applying streamline methods to very large geomodels
is the need for accurate and efficient solution of the pressure equation. In particular, the pressure solver must be locally (and globally) mass-conservative
and should handle: (i) irregular grids that conform to geological structures;
(ii) strongly heterogeneous and anisotropic formations; and (iii) flows with
large dynamic aspect ratios. Mixed finite element methods (MFEM) and
multi-point flux-approximation finite volume methods (MPFA) are examples
of methods that handle these properties, and cover the most widely used methods for elliptic problems where mass preservation is an issue.
In this talk we present a new simulation method for incompressible, immiscible two-phase flow on Cartesian grids that uses multiscale finite element
methods (MsFEM) to discretize pressure and velocities, and streamlines to
discretize fluid transport. High efficiency is obtained by solving the pressure
equation on a coarse grid, whereas the use of numerically constructed multiscale elements preserves the subgrid structures and gives mass-conservative
velocities that allows streamline computations to resolve fine flow patterns.
The main point in the talk is to indicate that the combination of multiscale
pressure solvers and streamline methods has a great potential for bridging
the gap between high-resolution geomodels and the capabilities of current
reservoir simulators.
Multi-Scale Finite-Volume Method for Multi-Phase Flow in Highly Heterogeneous Reservoirs
P. Jenny (Swiss Federal Institute of Technology)
Monday, 12:00–12:30, Hall 13
A multi-scale finite-volume (MSFV) method for multi-phase flow in highly
heterogeneous porous media was developed. In addition to a fine grid, the
method employs an imposed and a dual coarse grid. For the computation
of the fluxes across the interfaces of the imposed coarse grid cells and for
the reconstruction of the fine-scale velocity field two sets of basis functions
have to be constructed. These basis functions are local numerical solutions
reflecting the fine-scale heterogeneity of the permeability field. From the first
set of basis functions, which are computed on the dual coarse cells, effective
transmissibilities are extracted. These are used to obtain the coarse pressure
solution. Next, the fine-scale velocity field is reconstructed using the second
set of basis functions. This velocity field is then employed to solve the transport equations on the fine grid. For the coupling between flow and transport
an IMPES (implicit pressure, explicit saturation) scheme is applied. An im-
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portant feature of the MSFV method is the re-usability of the basis functions,
i.e. they do not have to be recomputed unless the accumulated change of total
mobility becomes locally too large. The MSFV method for multi-phase flow
and the scheme for the adaptive basis function updates will be explained in
detail. Moreover, the high accuracy and efficiency of the MSFV method will
be demonstrated for a variety of challenging test cases.
Stable and accurate simulation of multiphase flow in porous media
through separation of scales
R. Juanes (Stanford University)
Monday, 12:30–13:00, Hall 13
Multiscale phenomena are ubiquitous to flow and transport in porous media.
Such phenomena manifest themselves through at least the following three
facets:
1. The effective parameters in the governing equations are scale dependent.
2. The relevant physical processes may be different at different scales.
3. Some of the features of the flow (especially sharp fronts and boundary
layers) cannot be resolved on practical computational grids.
We employ a variational multiscale framework, which can potentially accommodate all three of the issues above. Here, we apply the multiscale formalism
to the accurate simulation of multiphase flow on coarse grids.
Under certain assumptions, the mathematical problem is expressed as an elliptic pressure equation, and an almost hyperbolic system of saturation equations. Both equations are coupled and highly nonlinear. We write the governing equations as a nonlinear system of conservation laws, expressed in weak
form. The key idea of the method is to decompose the pressure and the fluid
saturations into a coarse-scale component and a fine-scale component, which
leads to a rigorous multiscale split of the problem. Here, the subgrid scale
problem is approximated analytically using an algebraic approximation, and
the grid scale problem—which incorporates the subscale effects—is solved
using equal-order finite elements. This approach has been used before for
the finite element simulation of fluid mechanics problems. Here, we extend
it to be applicable to general systems of conservation laws. The crux of the
method relies on a proper definition of the matrix of intrinsic time scales,
which we design carefully after a stability analysis.
The performance of the method is illustrated with several representative
numerical simulations, involving water and gas injection in an oil reservoir.
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The results are compared with those obtained using the standard Galerkin
finite element method, and the upwind finite volume method.
Minisymposium: Dynamic Capillary Pressure Effects in Multi-Phase
Flow in Porous Media
I.S. Pop (Technische Universiteit Eindhoven)
Monday, 11:00–12:00, Hall 5
The difference between the individual fluid pressures in two-phase immiscible flow in porous media is characterized by the capillary pressure. The same
extends to multi-phase flow. Besides geometrical and physical properties of
the medium and of the fluids, usually the capillary pressure is assumed to depend on the phase saturations. This is valid under static conditions, but fails
when dynamical effects have to be talken into account, for example in case of
non-euilibrium imbibition or drainage.
In dynamic approaches the capillary pressure is assumed to depend also
on the time derivatives of the saturations. This leads to models that include
higher order terms with mixed time-space derivatives. Such models can explain effects that were observed experimentally, but are ruled out by standard porous media flow ones. An example in this sense are the nonmonotone
waves encountered in water driven oil recovery.
Within the minisymposium the discussions will focus on mathematical
questions (in particular analytical and numerical ones) posed by dynamical
capillary pressure effects. We expect that the participants will gain a better
understanding of the mathematical structure of these models, as well as new
open problems will arise.
Non-classical travelling waves for Buckley-Leverett via a pseudo-parabolic
degenerate regularisation.
C.M. Cuesta (Vienna University of Technology)
Monday, 11:00–11:30, Hall 5
We consider oil-water flow in porous media, with a dynamic capillary pressure relation. This leads to a pseudo-parabolic degenerate regularisation of
the Buckley-Leverett (B-L) equation of water-driven oil recovery. B-L is a
scalar conservation law with a convex-concave flux. The pseudo-parabolic
regularisation consist of a degenerate diffusive term, and a third order term
with mixed derivatives (first order in time, second order in space). It is wellknown that diffusive regularisations of B-L lead to admissible shocks that satisfy the Oleinik condition. However, linear pseudo-parabolic regularisation
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of B-L also admit shocks that violate the Oleinik condition, i.e. non-classical
shocks. Our aim is to clarify under which conditions degenerate non-classical
shocks are possible in this context. We therefore focus on the analysis of the
travelling wave equation. The degeneracy of the problem being the most intriguing property; it induces non-existence as well as non-uniqueness cases,
depending on the constitutive laws.
A new class of entropy solutions of the Buckley - Leverett equation
C.J. van Duijn (Technische Universiteit Eindhoven)
Monday, 11:30–12:00, Hall 5
The Buckley - Leverett equation describes two-phase flow in porous media.
For instance, enhanced oil recovery by water-drive. It is a first order hyperbolic conservation law with a nonlinear flux function of convex - concave
type. As a consequence, discontinuous or shock solutions may occur. Shock
solutions satisfy the weak form of the equation if and only if the Rankine Hugoniot condition across shocks is fulfilled. This expresses conservation of
mass and such shocks are called weak shocks.. For given initial and boundary data, many weak shocks are possible. This uniqueness problem is solved
by adding a small viscous term to the equation and by considering traveling
wave solutions of this regularized equation. A weak shock is admissible if it
arises as the limit of such traveling waves in the case of vanishing viscosity.
Such shocks are called weak entropy shocks. For a parabolic regularization,
i.e. adding effects of capillary pressure to the equation, this procedure leads
to the well-known Oleinik entropy condition.
In this contribution we demonstrate that this may not be the case if we
change the physics of the underlying regularized model. In particular, when
considering a model involving dynamic capillary pressure, we will construct
traveling waves yielding shocks that violate the Oleinik condition. These are
nevertheless correct entropy solutions corresponding to an improved description of the physics of the problem. This is joint work with L.A. Peletier.
Dynamic effect in capillary pressure-saturation relationships in unsaturated media and two-phase flow
S. Majid Hassanizadeh (Department of Earth Sciences, Utrecht University)
Monday, 12:00–12:30, Hall 5
Recent theories indicate that capillary pressure is perhaps not only a function
of saturation but may also depend on the time rate of change of saturation.
This is known as the dynamic or non-equilibrium effect. There is compelling
experimental evidence reported in the literature that the non-equilibrium effect is observable, quantifiable, and significant. However, almost all reported
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experiments relate to unsaturated systems. In this presentation, first the basic physics behind dynamic capillary effect is explained and experimental
evidences are presented. Next, we report on a recent series of experiments involving water and PCE. Quasi-static as well as a number of dynamic capillary
pressure curves, for primary drainage, main drainage and main imbibition, are
measured. The data are used to estimate the non-equilibrium capillary pressure coefficient. Finally, the potential significance of the dynamic effect in
the modeling of unsaturated flow and two-phase is discussed.
Minisymposium: Modern Industrial Statistics in the Industry
E.M. Jordaan (The Dow Chemical Company)
Monday, 11:00–13:00, Hall 7
Chemical, pharmaceutical and food manufacturers increasingly rely on information from measurements in the plants to ensure quality of products and
enable control. Using the knowledge effectively can lead to increased product quality, lower production costs and reduced risks. Engineers frequently
turn to statistics and mathematics to solve a variety of problems encountered
in manufacturing and R&D. We present a number of applications using stateof-the-art statistical techniques.
Risk Analysis - The asset mechanical reliability (AMR) is an important
factor in the asset utilization of production units. The AMR and the improvement can be quantified using statistical analyses such as: distribution analysis
of the contributing elements to the unreliability and Monte Carlo simulation
of the equipment configuration, including the intermediate storage capacity
and operating rules of the process.
Multivariate analysis of sensory data - One practical application of statistical techniques is the quality monitoring of the taste of coffee through multivariate analysis of sensory data. This includes factor analysis, multivariate
QC charts and multi-dimensional scaling on the basis of Mahalanobis distances.
Robust design using computer experiments - Computer experiments provide a unique opportunity for researchers, chemists and engineers to improve
product design and reduce time-to-market. This presentation will demonstrate, using case studies, how to combine robust design methodology with
Latin Hypercube designs and the fitting of emulators or metamodels. The
bottom line result is faster and better product development.
Recognition of Fungi Spores in Images - We use a model-based object
recognition method to identify airborne fungi spores in a digital microscopic
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image. The similarity measure measures the average angle between the
vectors of the template and the object. Model generation is done semiautomatically by manually tracing the object, automatic shape alignment,
similarity calculation, clustering and prototype calculation.
The application of reliability simulation in the process industry.
R.M. Dauwe (Dow Benelux)
Monday, 11:00–11:30, Hall 7
The asset utilization is closely monitored in most industries to come to grip
with improvements. Lost production can have multiple reasons and most
of them can be measured over time (e.g., loss in mechanical reliability and
controll, human error, raw material shortage, supply chain interference, etc.).
The first step in assessing this is by making distributions for the occurence
and the downtime (e.g. Weibull, normal, etc.) The second step is composing
a reliability block diagram consisting of all the items and in the manner they
are working functionally in the process. It is in fact a construction of the AND
and OR gates as in a fault tree. This includes as well all the storages involved
and the flows between the different units. The third step is running a Monte
Carlo simulation. In the results, the contribution can be seen to producton loss
of each of the items in the block diagram. Hence, the difference in production
loss can be quantified by any improvement action. Because of the nature
of Monte Carlo simulation, (as opposed to e.g. Markov analysis), this can
be done rather quickly and accurately and it helps the decision making. An
example will be given to illustrate this methodology.
Multivariate analysis of sensory coffee data.
G.D. Mooiweer (Sara Lee/DE)
Monday, 11:30–12:00, Hall 7
Senseo Crema is the revolutionary new coffeemaker of Douwe Egberts and
Philips. Using Senseo coffee pads it is possible to prepare one or two cups of
coffee within one minute. Compared to the traditional drip filter system these
Senseo coffee pads make it impossible to adjust the strength and taste of the
coffee by dosing more or less coffee. For this reason the basic assortment
Senseo coffee pads comprises three blends with increasing strength namely
Senseo Mild, Senseo Regular and Senseo Dark. It is important to maintain
the mutual strength of these blends despite natural variations in the applied
green coffees. As a practical application of statistical techniques this presentation will discuss the quality monitoring of the taste and strength of coffee
through multivariate analysis of sensory data. This includes factor analysis
and multivariate QC charts on the basis of Mahalanobis distances.
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Robust design using computer experiments
R.S. Kenett (KPA Ltd.)
Monday, 12:00–12:30, Hall 7
Computer experiments provide a unique opportunity for researchers, chemists
and engineers to improve product design and reduce Time To Market. This
presentation will demonstrate, using case studies, how to combine robust design methodology with Latin Hypercube designs and the fitting of emulators
or metamodels. The bottom line result is faster and better product development.
Model and Similarity-based Methods for the Recognition of Fungi Spores
in Images
P. Perner (Institute of Computer Vision IBaI)
Monday, 12:30–13:00, Hall 7
We propose and evaluate a method for the recognition of airborne fungi
spores. We use a model-based object recognition method to identify spores
in a digital microscopic image. The similarity measure measures the average
angle between the vectors of the template and the object. Model generation
is done semiautomatically by manually tracing the object, automatic shape
alignment, similarity calculation, clustering and prototype calculation.
Minisymposium: Examples of ECMI graduate student projects
M.P. Sørensen (Technical University of Denmark)
Monday, 11:00–13:00, Hall 4
The minisymposium presents shortly the ECMI educational system, implemented at the ECMI partner universities. Emphasis is on the 2 year postgraduate part with the two branches Technomathematics and Economathematics.
Beside courses in industrial and applied mathematics the students must spend
one semester abroad at an ECMI partner university, participate in a modelling
week and make a master thesis project on an industrial/economic problem.
The four speakers in the minisymposium are former ECMI students who
present their master thesis and current PhD-projects on industrial and applied
mathematics. The presentations illustrate a large span in subjects, from microelectronic industry, materials, cars, aerospace to geophysics and space research. The presentation on electronics deals with molecular dynamics simulation of the coating of a copper layer onto a silicon crystal. An example
from the automotive industry (Jaguar cars) is presented and one presentation
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is from aerospace industry in cooperation with Agusta-Westland helicopters.
The final talk concerns modelling of celestial paths of Near Earth Objects.
Detection and observation of Near Earth Objects are a priority subject in
space research and industry.
Optimal Prediction in Molecular Dynamics
B. Seibold (University of Kaiserslautern), H. Neunzert (University of
Kaiserslautern), T.G. Goetz (University of Kaiserslautern)
Monday, 11:00–11:30, Hall 4
A crucial step in the production of semiconductors is the coating of a copper
layer onto a silicon crystal. This process should be investigated by molecular dynamics simulations, which are typically very costly. The Fraunhofer
ITWM in Kaiserslautern is doing research on how to reduce the computational effort for such simulations. In my diploma thesis I invesigated whether
optimal prediction, a method to approximate the average solution of a large
system of ordinary differential equations by a smaller system, can be applied
in this field to speed up computations. A model problem is considered to
show how asymptotic methods can be employed to approximate the high dimensional conditional expectations, which arise in optimal prediction. The
thus derived smaller system is compared to the original system by MonteCarlo simulations, and it is shown under which conditions optimal prediction
yields a valid approximation to the original system.
Rattle in geared systems
C.K. Halse (University of Bristol), R.E. Wilson (University of Bristol), M.
di Bernardo (University of Bristol)
Monday, 11:30–12:00, Hall 4
Geared systems in various industrial applications, that normally operate quietly, have been shown to vibrate noisily at unpredictable times. We believe
this is due to the inherent backlash in geared systems. We demonstrate this
hypothesis with a simple model.
We model two meshing gears as a lightly damped single degree-of-freedom
oscillator with a piecewise-linear stiffness (a dead-zone nonlinearity). Along
with the ‘quiet’ solution, we show that there may also exist a variety of ‘rattling’ motions that can contact one or both sides of the dead-zone. We derive
asymptotically the boundaries of existence and stability for families of these
solutions.
Our work shows how the rattling solutions appear and in what parameter
regimes they can exist. We can use our conclusions to help eliminate unwanted behaviour.
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Monday Morning
Dynamics of a Helicopter Lag Damper
R.D. Eyres (University of Bristol)
Monday, 12:00–12:30, Hall 4
Lag dampers are used on helicopter blades to avoid resonant conditions as the
rotor increases in speed. In flight however the damper introduces undesirable
vibrations into the fuselage. The aim of this project is to passively reduce
the vibrations by changing the properties of the damper. The first stage is
to produce a parametric model of the damper and simulate the system. The
next step is to vary these parameters to find a way of reducing the vibrations
without having to use any external control mechanism.
Near-Earth Objects: Theory, Detection and Observation
S. Wolff (Technical University of Denmark)
Monday, 12:30–13:00, Hall 4
Near-Earth Objects are asteroids and comets having orbital parameters comparable to those of the Earth, such that their orbital motion leads to close
approaches with the Earth, thereby implying a risk of collision. GAIA
(http://astro.estec.esa.nl/GAIA/) is a proposed European Space Agency space
observatory (a satellite), aiming to measure the positions of an extremely
large number of celestial objects with unprecedented accuracy: remote galaxies and quasars as well as small asteroids within our solar system. In this
research project, the capability of GAIA will be exploited to detect and track
near-Earth objects.
Contributed presentations
Imaging Convex Inclusions in Uniform Conductors based on Electrical
Boundary Measurements
D. Roy (The University of Auckland)
Monday, 11:00–11:20, Hall 14
This paper focuses on simulation-based Bayesian inference from electrical
impedance tomography (EIT) data. Here we attempt imaging of an unknown
convex polygonal insulating inclusion within an object, otherwise made of
conducting material, using current/voltage measurements on the surface of
the object. This kind of problem can be classified as an inverse problem for
non-invasive imaging. In the forward map we solve a partial differential equation (PDE) subject to the boundary conditions. The statistical inverse problem
is to summarise the posterior distribution of conductance at all points within
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the image object given the current applied on the boundary of the object and
the corresponding potential generates on the boundary. In our work we apply
the sampling approach to EIT inverse problem using noisy simulation data.
This sampling is carried out using Markov chain Monte Carlo (MCMC).
Sound Scattering by a Spherical Object Near an Impedance Plane
M. Seyyed (Iran University of Science and Technology)
Monday, 11:20–11:40, Hall 14
The problem of acoustic scattering from a hard spherical body that is positioned near the locally reacting planar boundary is considered. The formulation utilizes the appropriate wave field expansions, the classical method of
images and the translational addition theorems for spherical wave functions
in combination with a simple local surface reaction model involving a complex amplitude wave reflection coefficient to simulate the pertinent boundary
conditions. The analytical results are illustrated with a numerical example in
which the spherical object is immersed near a layer of fibrous material set on
an impervious rigid wall, and is insonified by plane waves. The numerical
results reveal the important effects of interface local surface reaction, incident wave frequency, and scatterer position on the form function amplitude
and the far-field scattered pressure. Limiting case involving a spherical object
submerged near a hard flat boundary is considered.
Periodic Optimal Control Applications in Chemical Engineering
M. Diehl (University of Heidelberg), A. Toumi (Bayer Technology Services GmbH), D.B. Leineweber (Bayer Technology Services GmbH),
S. Engell (University of Dortmund), J.P. Schloeder (University of Heidelberg)
Monday, 11:40–12:00, Hall 14
We present numerical solution methods for periodic multi stage optimal control problems, and show how to apply them to problems in chemical engineering. The methods are based on the direct multiple shooting method for
optimal control that is briefly reviewed. A multistage formulation for optimal control problems with differential-algebraic equation (DAE) models and
multipoint constraints is introduced and illustrated.
In particular, the example of quasi periodic multiple fraction batch distillation with recycled waste cuts is considered. Here, a repeated batch distillation
is allowed to produce waste cuts each of which is then recycled in the following batch. The aim to find the best possible operating strategy results in a
quasi periodic optimal control problem. Optimization results are presented
and discussed.
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Second, a simulated moving bed chromatographic separation process is
considered. Here, switching of inlet and outlet ports leads to multiple stages
and periodicity. The large scale of the underlying DAE necessitates an special
problem formulation that can efficiently be treated within the framework of
multistage optimal control problems. Numerical results are presented and
discussed.
A Goodness of Fit Test For Linear Hypothesis In Nonparametric Regression Model
Z. Mohdeb (University Mentouri, Constantine), A. Mokkadem (University of Versailles)
Monday, 12:00–12:20, Hall 14
Consider the following model
Yi,n = f (ti,n ) + εi,n
i = 1, . . . , n ,
where f is an unknown real function, defined on the interval [0, 1] and t1,n =
0 < · · · < tn,n = 1 is a fixed sampling on [0, 1]. The errors εi,n form a
triangular array of independent random variables with zero mean and finite
variance σ 2 . Our aim is to construct linear hypotheses tests on the regression
function f in the case of a homoscedastic error structure. More precisely,
let x1 (t), . . . , x p (t) linearly independent functions in [0, 1] and let E p be the
vector space generated by x1 , . . . , x p ; we want to test the null hypothesis
H0 :
f ∈ Ep
against
H1 :
f 6∈ E p .
Concerning the problem of the hypotheses tests, the major part of the works
assume the regularity condition on f , x1 , . . . , x p ; generally these functions
satisfy the Hölder condition. In our approach, we assume that f , x1 , . . . , x p
are Riemann-integrable, and under this only condition on these functions, we
establish the asymptotic weak behavior of the proposed test statistic, then we
have the level and the asymptotic power of the test. A simulation study is
conducted to check the validity of the asymptotic result in a Monte Carlo
experiment.
Statistical thermodynamics for choice models on graphs.
A. Majka (ICM), W.W Wislicki (ICM)
Monday, 12:20–12:40, Hall 14
This talk is related to choice models which are of great importance for many
branches of economics, psychology, the behavioral sciences, cognitive science, political science and the social sciences. In discrete choice models, one
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Monday Morning
assumes that there exists the choice set consisting of a countable and finite set
of comparable alternatives. These are related to the preferences of each decision maker, what mathematically is described by the so-called utility function.
It is itself a random variable for which probability density function has been
found. We showed the analogy between the properties of the utility and the
total energy functions of finite physical systems, thus enabling applications
of thermodynamic formalism to economic systems. We develop equilibrium
thermodynamics in the framework of the canonical and the grand canonical
ensembles. We applied our approach to communication networks focusing
on airline markets. This project has been done with cooperation with Boeing
Commercial Airplanes.
The results have been submitted to publication in Physica A.
Multi-Threaded Application of Monothetic Clustering Method
G. Brunet (IUT-STID)
Monday, 12:40–13:00, Hall 14
In this paper a method is presented for using concurrent programming to perform a divisive hierarchical clustering. A monothetic clustering technique has
been developped to obtain a fast and reliable classification with building of a
binary tree. Multi-threaded programming has been achieved with Java as support language and an algorithm has been obtained with techniques for solving
the synchronization and communication problems. The proposed clustering
has the advantages to be simple and fast. Applied to a set of points, it performs simultaneously a hierarchy of the set and a characterization of each
cluster with a conjunction of logical properties.
Monday Morning
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Monday Afternoon
Monday Afternoon
14:00–15:00
Alan Tayler Lecture
Modelling processes in the glass industry (J. Hinch) . . . . . . . . . . . . .
15:00–15:30
Break
15:30–17:30
Scientific Computing Perspectives in Micro and Nano-Electronics (J.A.
Carrillo; theme: Electronic industry) . . . . . . . . . . . . . . . . . . . .
A PDAE-Model for Thermal-Electric Coupling in Chip-Design (A. Bartel) .
An Improved Method to Determine the Noise Performance of Submicrometer Self Aligned Bipolar Transistor (S. Rinaudo) . . . . . . . . . . . . . .
Coupled device, circuit and interconnect simulation (W.H.A. Schilders) . . .
Modelling and simulation of nanoscale electron devices (X. Oriols) . . . . .
Nonlinear Model Predictive Control (M. Diehl; theme: Chemical technology)
Nonlinear Model Predictive Control of Batch Processes (K. Nagy) . . . . . .
Optimization-based Control of a Reactive Simulated Moving Bed Process
for Glucose Isomerization (A. Toumi) . . . . . . . . . . . . . . . . . . .
Sensitivity-based solution updates in closed-loop dynamic optimization (J.
V. Kadam) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
On-line optimization of the start-up of steam boilers in closed loop (R. Franke)
NMPC of a hybrid continuous-batch process (C. de Prada) . . . . . . . . . .
Mathematical Methods in Polymer Flow Simulation (J. Molenaar; theme:
Materials) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mathematics and Rheology: An Introduction (J. Molenaar) . . . . . . . . .
Entanglements in polymer melts (W.J. Briels) . . . . . . . . . . . . . . . . .
The CRAFT tube model: a new constitutive equation for blends of entangled
linear polymers (R. Keunings) . . . . . . . . . . . . . . . . . . . . . . .
Direct simulations of particle suspensions in a viscoelastic fluid in sliding
periodic frames (M.A. Hulsen) . . . . . . . . . . . . . . . . . . . . . . .
Mathematical Models for Enhanced Oil-Recovery (C.J. van Duijn; theme:
Geophysics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Gravity counterflow segregation with permeability hysteresis (D.M. Marchesin)
Gravity segregation in homogeneous reservoirs (W.R. Rossen) . . . . . . . .
Mathematical modelling of gel-placement in porous media (F.J. Vermolen) .
Travelling waves in a finite condensation rate model for steam drive recovery
of oil (J. Bruining) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Monday Afternoon
Forward and Inverse Problems in Multiphase Flow through Porous Media
(S.B. Hazra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Applications of non-isothermal multiphase multicomponent models for flow
and transport in porous media (H. Class) . . . . . . . . . . . . . . . . . .
Numerical Methods for Two-Phase Flow in a Porous Medium With Two
Rock Types (J.E. Roberts) . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation of Flow and Transport in Heterogeneous Porous Media (P. Bastian)
Numerical Parameter Identification in Multiphase Flow through Porous Media (S.B. Hazra) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation-based optimization in industry (H.P. Stehouwer) . . . . . . . .
Optimisation of a stamping process using FEM simulations (E.H. Atzema) .
COMPACT-CO: an integral meta-modeling approach (E.D. Stinstra) . . . . .
Simulation-based optimisation in the semiconductor industry (J.H.J. Janssen)
Robust CRT shadow mask optimization using COMPACT-CO (J.W.J.M. van
der Heijden) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
On a Constrained Nonlinear Optimization Problem for Preventing Hot
Cracking in Laser Beam Welding (V. Petzet) . . . . . . . . . . . . . . . .
Defects in Object Detection by the Cone Beam Tomography Method in the
Presence of Noise (O.E. Trofimov) . . . . . . . . . . . . . . . . . . . . .
A Stabilized Chebyshev -Spectral Approach for a Class of Nonlinear OrrSommerfeld Eigenvalue Problems (I. Gheorghiu) . . . . . . . . . . . . .
Gradient Computations for Optimal Design of Turbine Blades (K. Arens) . .
Fast Shape Design for Industrial Components (E.H. Lindner) . . . . . . . .
A New Model for the Unsteady Expansion and Contraction of a Long TwoDimensional Vapour Bubble Confined Between Superheated or Subcooled
Parallel Plates (K. Das) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scattering of sound waves by a spherical poroelastic shell near a planar
boundary (M. Seyyed) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Modelling processes in the glass industry
J. Hinch (University of Cambridge)
Monday, 14:00–15:00, Blauwe Zaal
1. Fibre production by a jet dropping from a furnace onto two fast counterrotating drums, producing glass wool.
2. Levitation of a gob of molten glass on an air cushion, with rim waves
and instabilities.
3. Spreading of a blanket of melting raw materials, or foam, over the convecting bath.
H7
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Monday Afternoon
Minisymposium: Scientific Computing Perspectives in Micro and
Nano-Electronics
J.A. Carrillo (ICREA-UAB), A. Majorana (Universita di Catania)
Monday, 15:30–17:30, Hall 11
This minisymposium is focused on several problems in the simulation and
modelling of electronic components. The main aim is to bring together people at academia and industry to discuss about particular aspects of the huge
world of nanoelectronics focusing on numerical algorithms for transport in
nanocomponents, modelling of heat conduction in chip-design and electrical
components based on new materials. Simulation tools and commercial software are available to electrical engineers based on models that typically break
down in the new electric components due either to their size, the thermal coupling or the new material structure. We want to contribute in depicting new
directions in nanoelectronics in which eventual industrial projects may appear.
A PDAE-Model for Thermal-Electric Coupling in Chip-Design
A. Bartel (Bergische Universität Wuppertal)
Monday, 15:30–16:00, Hall 11
Advances in chip-technology are partly obtained by the miniaturization of
basic semiconductor devices. Therefore former secondary effects such as
heat conduction come into play – transistors start to recognize neighbors thermally. This situation is aggravated in the recent SOI-technology (silicon-oninsulator). Due to strongly temperature dependent mobilities, the thermalelectric coupling is important for the reliability of circuit designs.
To obtain a model which takes heat conduction into account, but enables (at
the same time) an efficient numerical treatment in the industrial circuit simulator, the accompanying thermal network (AN) is introduced. This model
integrates the heat conduction along one-dimensional macro-structures and
supplies zero-dimensional thermal elements for the usual lumped-thermal approach. Now, the coupling of the differential algebraic network equations
for the electric part and the description of the AN yields a system of partial
differential-algebraic equations, a PDAE.
In this talk, the setup and the validity of this coupled system is briefly
discussed. Then we address the numerical co-simulation of that PDAE. This
naturally enables the add-on of thermal effect to the industrial simulators and,
furthermore, it can be designed to exploit the multirate potential. At the end,
we investigate an example circuit.
Monday Afternoon
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An Improved Method to Determine the Noise Performance of Submicrometer Self Aligned Bipolar Transistor
S. Rinaudo (STMicroelectronics)
Monday, 16:00–16:30, Hall 11
This paper presents an approach to get a full characterization of microwave
bipolar transistors starting from S-parameters measurement only. The analytical form of the Y-matrix representation is derived starting from the π-hybrid
model and it is used to directly and accurately extract all the parameters of
the model. All the parameters of the small-signal model are determined directly from S-parameters. (We measure S-parameters, but all the other set of
two-port network parameter, which we use in this technique, as Z and Y, are
determined using conversion formulae.) In this way, we are able to determine
a physic small-signal model, that enable to represents the two-port network
parameters and to describe the device structure. Once we know an equivalent
model, we are able to compute the noise performance, adding the well known
noise source of the bipolar devices. In the second part of the paper the noise
sources are added to the equivalent model, and the analytical expression of
noise figure is obtained. This expression is used to obtain a full set of noise
parameters to characterize the behaviour of the bipolar microwave transistors.
Coupled device, circuit and interconnect simulation
W.H.A. Schilders (Technische Universiteit Eindhoven)
Monday, 16:30–17:00, Hall 11
Until recently, simulation software was produced for various problems in the
electronics industry, ranging from process and device simulation to circuit
simulation. Due to the continued miniaturization and the use of higher frequencies, nowadays there is a growing need for a coupled analysis of problems in the electronics industry. Process and device simulation have already
been coupled in so-called TCAD environments, but the coupling of semiconductor device and circuit simulation has started only recently. In addition,
because of the effects menboned before, electromagnetic effects are starting
to play an important role in the design of circuits: it can no longer be assumed
that the wires used for conducting the currents are ideal. There will be delays due to interactions between neighbouring wires. A full electromagnetic
analysis is also complicated by the fact that state-of-the-art designs contain
up to 7 or 8 layers in which the wires are located. In this presentation, we will
discuss the coupling of device, circuit and electromagnetics simulations, and
the mathematical tools needed to achieve an efficient way of achieving this.
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Monday Afternoon
Modelling and simulation of nanoscale electron devices
X. Oriols (Universitat Autonoma de Barcelona)
Monday, 17:00–17:30, Hall 11
Advanced research in nanoscale devices is now targeted towards technologies
below 20 nm. At such small dimensions, the wave nature of electrons leads
to the appearance of important Quantum Mechanical (QM) phenomena. We
will focus our talk on some open problems for the modelling and simulation
of such nanoscale electron devices.
First, we will discuss the difficulties in studying current noise on nanoscale
devices. Within our approach (we propose the use of QM trajectories [1]),
the possibility of simultaneously dealing with the wave and particle nature
of electrons provides a simple understanding of noise phenomena in the QM
regime, that can be very salutary for nanoelectronic engineers. Numerical
studies for current noise in tunnelling heterostructure devices will be presented [2].
Second, we will analyze how QM effects determine the high (>GHz) frequency behaviour of mesoscopic systems. For such AC conditions, electron
transport properties are determined by the spatial and also by the temporal
phase-coherence of electrons. Numerical results for the study of the ultimate
high-frequency quantum limit for the transconductance of 15 nm double gate
MOSFET will be presented [3].
[1] X.Oriols et al. Appl. Phys. Lett. 79, 1703 (2001)
[2] J.Suñé and X. Oriols, Phys. Rev. Lett., 85, 894 (2000); X. Oriols et al. Appl.
Phys. Lett. 80,4048 (2002); X.Oriols IEEE Transaction on Electron Devices,
50, 1830, (2003).
[3] E.Fernandez-Diaz, A.Alarcon and X.Oriols. (to be published)
Minisymposium: Nonlinear Model Predictive Control
M. Diehl (University of Heidelberg)
Monday, 15:30–18:00, Hall 4
Nonlinear Model Predictive Control (NMPC) is an emerging feedback control technique that uses a nonlinear dynamic process model for online optimization of predicted future process behaviour. By performing this prediction
and optimization repeatedly on a moving horizon, NMPC allows to provide
feedback to disturbances and to perform setpoint changes efficiently. Major
advantages of the technique are the possibility
Monday Afternoon
43
• to use available process models in form of nonlinear ordinary differential or algebraic-differential equations
• to incorporate constraints on controls or states, and
• to formulate control objective functions that reflect economic criteria.
Challenges for industrial NMPC applications comprise the reliable solution
of large scale nonlinear optimal control problems in real-time, online state
and parameter estimation, stability of the closed loop, and the question of
robustness and how to address model-plant mismatch.
In recent years, academic and industrial research has achieved major
progress in these areas, and first industrial applications of NMPC are reported. Aim of the minisymposium is to reflect the current state of NMPC
research, in particular from an application perspective. All participating scientists are distinguished by important contributions in the area of NMPC and
applications, from academia and industry.
Nonlinear Model Predictive Control of Batch Processes
K. Nagy (University of Stuttgart), R. Findeisen (University of Stuttgart), F.
Allgöwer (University of Stuttgart)
Monday, 15:30–16:00, Hall 4
Trends in process industries toward high value products have increased the
interest in the optimal operation of batch processes. The highly competitive nature of these industries, and the strong nonlinearities of the systems
have generated an increased interest toward nonlinear model predictive control (NMPC) approaches. NMPC uses nonlinear model to predict the behavior of the process, and determines a sequence of optimal control inputs with
respect to some objective. In the case of batch processes the real economic
objective is usually related to the product quality at the end of the batch, leading to a shrinking horizon formulation of the control problem. In practical
model based control applications robustness against model/plant mismatch
need to be considered. The synthesis of robust NMPC control laws usually
deals with the determination of the best open-loop control trajectory under
uncertainties or disturbances. Robustness is achieved by formulating the optimization problem in a game-theoretical framework, when two conflicting
terms in the problem account for performance and robustness, respectively.
Mathematically, this can be achieved by either solving a minmax dynamic
optimization problem, or formulating the robust control problem as a multiobjective optimization problem, where one part of the objective function
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Monday Afternoon
accounts for nominal performance while the other for robustness. The openloop formulation of the robust NMPC may be very conservative, since only
open-loop control is used between sampling times. This may lead to lower robust performance or even unfeasible problems in certain disturbance scenarios, since disturbances are not directly rejected between the sampling times.
The keystone in the framework used here is that the aforementioned multiobjective optimization problem searches for feedback strategies not open-loop
controls, thus providing increased robustness, against disturbances and parameter uncertainties. The increased robust performance, and greater computational complexity of these approaches will be assessed using a simulated
industrial batch process.
Optimization-based Control of a Reactive Simulated Moving Bed Process for Glucose Isomerization
A. Toumi (University of Dortmund)
Monday, 16:00–16:30, Hall 4
In this work, the production of High Fructose Corn Syrup (HFCS) in a Reactive Simulated Moving Bed (RSMB) is considered (Toumi and Engell, [1],
2004). The RSMB process combines a quasi-continuous chromatographic
process with an enzymatic biochemical conversion of glucose to fructose.
This process is characterized by complex dynamics with discrete decisions.
The objective is to maintain a high product purity while minimizing the eluent
consumption (Toumi and Engell, [2], 2004 ).
A sequential optimization approach is applied in order to determine the
optimal operation of the real plant.
The performance of the process parameters is further improved by varying
the column length (VARICOL) over the zones of the RSMB plant and manipulating the flow rates by a nonlinear model predictive controller NMPC
in order to control the purity requirements of HFCS (Toumi and Engell, [3],
2004).
[1] A. Toumi and S. Engell: Optimal Operation and Control of a Reactive Simulated Bed Process, International Symposium on Advanced Control of Chemical
Processes (2004), ADCHEM, pp. 243-248.
[2] A. Toumi and S. Engell: Optimierungsbasierte Regelung eines integrieten reaktiven Trennprozesses, AT-Automatisierungstechnik 52 (2004), pp. 13-22
[3] A. Toumi and S. Engell: Optimization-based Control of a Reactive Simulated
Moving Bed Process for Glucose Isomerization, submitted to Chemical Engineering Science (2004).
Monday Afternoon
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Sensitivity-based solution updates in closed-loop dynamic optimization
J. V. Kadam (Process Systems Engineering, RWTH Aachen), W. Marquardt (Process Systems Engineering, RWTH Aachen)
Monday, 16:30–17:00, Hall 4
Increasing competition requires a more agile chemical plant operation. This
demands an integration of economic optimization and control. However, existing applications use either stationary real-time optimization or off-line dynamic optimization together with linear model-based control. Off-line dynamic optimization and trajectory tracking is not fully satisfactory for online application in the plant due to uncertainty. In the last decade, nonlinear
model-predictive control (NPMC) with output feedback has been developed
significantly. The challenge for these real-time optimization-based control
systems is to efficiently handle uncertainty. We consider a closed-loop dynamic real-time optimization (D-RTO) approach that improves economic objective, which is structurally identical to NMPC. The inherent limitation of
slow-feedback in D-RTO due to higher computational expense can lead to
sub-optimal or infeasible plant operation. A novel approach for closed-loop
optimization is presented that systematically combines a fast update-strategy
with rigorous optimization when necessary. This addresses the key issues of
efficiency, accuracy of real-time solution updates. A parametric sensitivitybased technique is used to calculate optimal first-order updates to a nominal
reference solution. The technique does not assume that the active constraint
set remains the same after changes in uncertain parameters. In closed-loop,
the approach is very effective to handle uncertainty while requiring only a
minimum number of full real-time optimizations reducing the on-line computational expense. The approach is illustrated by simulations of closed-loop
real-time optimizations of a semi-batch reactor described by a model with
different kinds and ranges of parametric uncertainty. It is observed that the
closed-loop updated solution is almost identical to the true optimal solution
corresponding to uncertainty.
On-line optimization of the start-up of steam boilers in closed loop
R. Franke (ABB Corporate Research), K. Krüger (ABB Utility Automation
GmbH)
Monday, 17:00–17:30, Hall 4
Nonlinear model based predictive control (NMPC) is applied to minimizing startup time and costs of steam boilers subject to constraints on thermal
stresses. It has been known from theory for many years that an optimal startup drives the process along its thermal stress constraints. Nevertheless such
a control was never achieved applying alternative control technologies so far.
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The control problem is multi-variable, non-linear, exhibits output constraints,
and relies on a sufficient prediction of the process behaviour.
During on-line optimization in closed loop, one high-dimensional nonlinear optimization problem is solved every minute. Starting from the current
process state, the optimal operation is predicted based on a rigorous physical
process model. The calculated control is applied to the process.
The new startup solution is currently being deployed in a 700 MW block
of a coal fired power plant. The contribution focusses on issues experienced
during the practical application of on-line optimization in closed loop. Useful results for the immediate control actions produced by the NMPC strongly
rely on the appropriate consideration of plant/model mismatch and on a sufficiently long prediction horizon. Numerically, the exploitation of the sparse
structure of the high-dimensional constrained optimization problem is crucial
to fulfill real-time requirements.
NMPC of a hybrid continuous-batch process
C. de Prada (University of Valladolid), D. Sarabia (University of Valladolid), SC Smaranda Cristea (University of Valladolid)
Monday, 17:30–18:00, Hall 4
This paper deals with the control of mixed process plants where a part operates continuously while other units are batch ones. This kind of processes
needs to maintain some (continuous) variables at prescribed values and, at the
same time, choosing the operation times of the batch units. More precisely,
we consider the problem of operation of a small lab plant where a couple of
temperature and level tanks interact with two batch units following a given
sequence of stages, from a process control perspective. Here the timing and
scheduling of the operation is a key factor combined with continuous control.
The problem refers to a small pilot plant but it has the relevant characteristics
of an industrial scale setup of many process factories where a significant number of bottleneck problems occur. The standard control approach, based on a
continuous process model and continuous manipulated variables, fails due to
the discrete (integer) or logical nature of the new elements. In the same way,
scheduling of the batch units alone cannot cope with the regulatory control of
other variables. It is then important to reformulate the control problem finding adequate representations of this hybrid system as well as practical paths
to solve and analyse it. The aim of the paper is to present a formulation using
the predictive control framework as well as some results of its operation.
Monday Afternoon
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Minisymposium: Mathematical Methods in Polymer Flow Simulation
J. Molenaar (Technische Universiteit Eindhoven), R. Keunings (Universite
catholiquede Louvain), W. Briels (University Twente)
Monday, 15:30–17:30, Hall 12
Since around 1950 plastics were introduced in industrial applications, the
production of these synthetic materials has grown exponentially. During the
forming of plastics products, polymer melts are processed. Polymer flows
have very unusual properties due to their special microstructure. The long
molecular chains have interactions that are nearly completely determined by
topological constraints: the movement of a specific chain is hindered by its
neighbours. A succesful way to picture this dynamics is to describe it as
if a snake slides in a tube. This special type of modelling leads to special
mathematical methods. This minisymposium gives an overview of various
methods. The first presentation is of an introductory nature to introduce the
concepts used in this field. In the other lectures well-known experts in the
field present different approaches, which ususually lead to huge numerical
simulations. The complexity of these calculations has led to the development
of several new numerical methods in order to keep the calculation times under
control.
Mathematics and Rheology: An Introduction
J. Molenaar (Technische Universiteit Eindhoven)
Monday, 15:30–16:00, Hall 12
Since around 1950 plastics were introduced in industrial applications, the
production of these synthetic materials has grown exponentially. During the
forming of plastics products, polymer melts are processed and these flows
have very unusual properties due to their special microstructure. This field of
study is called ’rheology’. The long molecular chains have interactions that
are nearly completely determined by topological constraints: the movement
of a specific chain is hindered by its neighbours. A succesful way to picture
this dynamics is to describe it as if a snake slides in a tube. This special type
of modelling makes use of a great variety of mathematical methods. In this
introduction the concepts of rheology are dealt with, so that the audience gets
acquainted with the ideas and terminology used in the other lectures of this
mini-symposium.
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Entanglements in polymer melts
W.J. Briels (University of Twente)
Monday, 16:00–16:30, Hall 12
Since the interesting time and length scales in polymers are extremely long,
direct atomistic simulations are infeasible; if not followed up by a coarse
grain analysis, they would even be non-instructive. As a consequence we
have to develop coarse grain simulation methods to speed up the computations and to address the right time and length scales. I will present a coarse
graining procedure, which I recently developed with J.T. Padding, and that we
successfully applied to study the rheological properties of polyethylene melts.
We started from an atomistic simulation of relatively short chains, from which
we calculated all the parameters needed for mesoscopic Brownian dynamics
simulations of much longer chains. By doing so, interactions at various length
and time scales come out naturally without being implemented by the modeller. All characteristic times and lengths occurring in different properties of
the melt are fully consistent with each other and all results are in agreement
with experimental results. A natural thing to demand from coarse grain models is that they should allow the calculation of all properties of the underlying
system that can be described in terms of the surviving coarse variables. In
principle the pressure is among these properties. As a result of additional
approximations however the proposed method, although describing the rheological properties extremely well, does not reproduce the pressure. I will
briefly comment on the reasons for this.
The CRAFT tube model: a new constitutive equation for blends of entangled linear polymers
R. Keunings (Université catholique de Louvain), A. Leygue (Université
catholique de Louvain), C. Bailly (Université catholique de Louvain)
Monday, 16:30–17:00, Hall 12
We present and evaluate the CRAFT chain model (Constraint Release Average Tensorial Full Chain Model), namely a new constitutive equation for
blends of entangled linear polymers. The model is built upon a tensorial expression for a full chain representation of the microstructure. Reptation and
stretch relaxation mechanisms are accounted for, while both thermal and convective constraint release are introduced in a unified formulation.
Due to the connectivity of tube segments, the proposed constitutive equation has the form of a set of coupled partial differential equations formulated
along the tube axis. The numerical predictions of the model are computed using a finite difference discretisation, leading to a coupled multimode system.
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The proposed formulation of constraint release can be extended to the case
of polydisperse systems to provide a mixing rule which, in the linear regime,
is equivalent to the mixing rule of double reptation.
Predictions of the CRAFT model in various rheometrical flows are presented for monodisperse and bidisperse systems and are compared with experimental results.
Direct simulations of particle suspensions in a viscoelastic fluid in sliding
periodic frames
M.A. Hulsen (Technische Universiteit Eindhoven), W.R. Hwang (Technische Universiteit Eindhoven), H.E.H. Meijer (Technische Universiteit
Eindhoven)
Monday, 17:00–17:30, Hall 12
We present a new finite element scheme for direct simulation of particle suspensions in simple shear flow of viscoelastic fluids in a well-defined periodic
domain in simple shear flow [1,2]. The governing equations are discretized
using the DEVSS method for the momentum equation and the discontinuous Galerkin method for the constitutive equation. Furthermore, we employ
(i) the sliding periodic frame concept of Lees & Edwards [J. Phys. C 5
(1972) 1921] in order to eliminate complicated wall effects; (ii) the rigid-ring
(rigid-shell in 3D) description for the particle, which allows easy treatment of
boundary-crossing particles. Both the sliding-frame and rigid-ring contraints
are imposed by Lagrangian multipliers.
We discuss flow-induced microstructural developments, emphasizing molecular conformation of polymers (how they orient and stretch in suspensions),
as well as the bulk suspension properties. In 2D simulations, we find shearthickening behavior of the bulk shear viscosity and the first normal stress coefficient, kissing-tumbling-tumbling phenomena of closely-located two particles (clustering of two particles) and the development of strongly oriented
elongational flow between separating particles [2].
We are currently extending our method to 3D systems and hope to present
at the conference some first results with spherical particles in sliding triperiodic domains of simple shear flow.
[1] W.R. Hwang, M.A. Hulsen, H.E.H. Meijer, “Direct simulation of particle suspensions in sliding bi-periodic frames,” Journal of Computational Physics Volume
194, Issue 2 , 2004, 742
[2] W.R. Hwang, M.A. Hulsen, H.E.H. Meijer, “Direct simulations of particle suspensions in a viscoelastic fluid in sliding bi-periodic frames,”, JNNFM.
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Minisymposium: Mathematical Models for Enhanced Oil-Recovery
C.J. van Duijn (Technische Universiteit Eindhoven), J. Bruining (Delft
University of Technology)
Monday, 15:30–17:30, Hall 13
In this minisymposium the four speakers will present and analyse models describing some of the most well-known techniques for enhanced oil recovery.
Specifically, models for gel-placement and for water, steam and foam drive
will be presented. In mathematical terms, each of the models uses a formulation in terms of hyperbolic partial differential equations (conservation laws).
Gravity counterflow segregation with permeability hysteresis
D.M. Marchesin (IMPA- Instituto Nacional de Matematica, Rio de Janeiro),
C.E.S. Schaerer (IMPA- Instituto Nacional de Matematica), M. Sarkis
(IMPA- Instituto Nacional de Matematica)
Monday, 15:30–16:00, Hall 13
Hysteresis phenomena have been long recognized in laboratory experiments
to have significant effects on two phase flow in porous media. In this paper we
develop a novel numerical scheme to account for the permeability hysteresis
effect, and we apply it to the gravity counterflow segregation problem. The
scheme is based on associated local Riemann solutions and can be viewed as
a modification of the classical Godunov method.
The Riemann problem solutions necessary for the scheme are presented
and analyzed. The numerical results show the strong influence of the hysteresis phenomenon on the flow and recover qualitatively and quantitatively the
saturation profiles obtained in laboratory experiments in the literature.
Gravity segregation in homogeneous reservoirs
W.R. Rossen (The University of Texas at Austin), W.R. Rossen (The University of Texas at Austin), C.J. van Duijn (Technische Universiteit Eindhoven)
Monday, 16:00–16:30, Hall 13
The model of Stone (1982) for gravity segregation in steady, horizontal gasliquid flow in a homogeneous reservoir is extremely useful and apparently
general, but without a sound theoretical foundation. The model has fit simulations of simultaneous injection of gas and liquid, and also of foam, into
rectangular and cylindrical reservoirs in a wide variety of cases. The implications of the model are profound: for instance, for a given reservoir and density difference between phases, the only way to increase the distance gas and
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water travel together before complete gravity segregation is to increase the
injection-well pressure. This conclusion applies also to continuous-injection
foam processes, with some restrictive assumptions. Stone makes the standard assumptions of fractional-flow theory (incompressible phases, Newtonian rheology, immediate attainment of local steady state), but no proof of this
model based on fractional-flow theory has been presented. Here we present
a proof that this model applies to steady-state gas-liquid flow, and also foam
flow, if the standard assumptions of fractional-flow theory are made. We solve
for the lateral position of the point of complete segregation of gas and water
flow, but there is still no rigorous solution for the curves separating override,
underride and mixed zones, or for the vertical height of the position of complete segregation.
Mathematical modelling of gel-placement in porous media
F.J. Vermolen (Delft University of Technology), J. Bruining (Delft University of Technology), C.J. van Duijn (Technische Universiteit Eindhoven)
Monday, 16:30–17:00, Hall 13
In this paper we analyze advective transport of polymers, crosslinkers
and gel, taking into account non-equilibrium gelation, gel adsorption and
crosslinker precipitation under a constant pressure drop. In absence of diffusion/dispersion the resulting model consists of hyperbolic transport-reaction
equations. These equations are studied in several steps using analytical and
numerical techniques. For simple cases, we obtain explicit travelling wave solutions, whereas for more complicated cases we rely on analytical techniques
to analyse the problem qualitatively. Finally, a numerical solution for the full
system of equations is obtained. The results developed in this study can be
used to validate numerical solutions obtained from commercial simulators.
Travelling waves in a finite condensation rate model for steam drive recovery of oil
J. Bruining (Delft University of Technology), C.J. van Duijn (Technische
Universiteit Eindhoven)
Monday, 17:00–17:30, Hall 13
We formulate a hyperbolic model of steam drive displacement of oil in porous
media. The present contribution builds on previous work where we assumed
a local thermodynamic equilibrium model. Now we use a condensation rate
equation with a finite rate constant. Disregarding capillary pressure away
from the condensation zone, a 2x2 hyperbolic system arises for the water
and steam saturation. This system cannot be solved uniquely without additional conditions at the SCF. To find such conditions we blow up the SCF
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and consider a parabolic transition model, including capillary diffusion and
a finite condensation rate. We show numerically and using a color map that
our choice of the condensation rate equation leads to a unique solution in the
hyperbolic limit. Also we discuss a proof that the rate equation tends to thermodynamic equilibrium in the limit of a large rate constant. We end with
computations for some realistic cases. Contrary to our expectation it appears
that the solution (from the numerical point of view) is independent of the rate
constant in the condensation model.
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Minisymposium: Forward and Inverse Problems in Multiphase Flow
through Porous Media
S.B. Hazra (University of Trier), V. Schulz (University of Trier)
Monday, 15:30–17:30, Hall 5
Modeling and computation of multiphase flow through porous media has got
wide applications in various fields of science and technology. With the advancement of computer technology and availability of robust numerical techniques, more and more sophisticated models are being developed. With the
increase of model sophistication, the number of parameters involved in these
models is becoming bigger. In this minisymposium the speakers will discuss
about recent developements in terms of sophisticated models and advanced
computational tools for solving the model equations as well as finding the
parameters involved in the models.
Applications of non-isothermal multiphase multicomponent models for
flow and transport in porous media
H. Class (University of Stuttgart), A. Bielinski (University of Stuttgart),
S.O. Ochs (University of Stuttgart)
Monday, 15:30–16:00, Hall 5
The modelling of multiphase processes in porous media gains increasing
relevance for many different applications. This covers environmental (e.g.,
subsurface/groundwater contamination and remediation), technical (e.g., enhanced oil recovery) and industrial (e.g., fuel cells) fields. In this presentation,
some special applications of multiphase multicomponent simulators for processes in the subsurface will be addressed. The first one deals with The second topic addresses the recently discussed technique of CO2-sequestration
into geologic formations as a means to reduce the concentration of greenhouse gases in the atmosphere. There is currently intensive research going on
to investigate the efficiency, sustainability, and the long-term consequences
to the environment concerning the storage of CO2, for example, in depleted
hydrocarbon reservoirs, saline aquifers, or unmineable coal seams. The processes occurring thereby include the fluid phases water resp. brine and gas,
where the main component in the gas phase is CO2. Depending on the pressure and temperature conditions, the mass components can be transferred between the phases according to the phase/component equilibria. Furthermore
it is characteristic to the CO2-sequestration problem that the pressure and
temperature conditions are around the critical point of CO2. Thus, it is essential to develop approaches that allow a good quantitative approximation
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of the phase behaviour and the strongly varying fluid properties.thermally enhanced remediation of NAPL-contaminated soils. In this context, the usage
of sophisticated numerical modelling techniques is a powerful means to gain
improved understanding of the coupled physical processes and to support the
development and optimization of remediation technologies like, for example, steam flooding, thermal wells, soil air extraction, etc. The application of
a non-isothermal multiphase multicomponent model concept accompanying
experiments on different scales in the VEGAS groundwater research facility
at the University of Stuttgart, Germany, will be presented.
Numerical Methods for Two-Phase Flow in a Porous Medium With Two
Rock Types
J.E. Roberts (Inria-Rocquencourt), J. Jaffré (Inria-Rocquencourt)
Monday, 16:00–16:30, Hall 5
Incompressible two-phase flow in porous media are modelled by a set of nonlinear equations whose nonlinear coefficients depend on capillary pressure
and relative permeabilities. A model with two rock types is one that has an
interface where the capillary pressure and relative permeability curves change
due to a rock change. Using cell-centered discretization techniques we discuss flux calculations at this interface both for the case in which capillary
pressure is taken into account and for the case in which it is not.
Simulation of Flow and Transport in Heterogeneous Porous Media
P. Bastian (University of Heidelberg)
Monday, 16:30–17:00, Hall 5
Most natural porous media are heterogeneous and understanding the flow in
such media is highly important in such diverse fields as groundwater remediation, atomic waste repositories and petroleum reservoir engineering. The
use of numerical methods to simulate flow and transport in porous media has
become standard. In this talk we develop and compare two relatively new
numerical methods, the Discontinuous Galerkin method (DG) and Eulerian
Localized Adjoint methods (ELLAM).
DG methods use trial and test functions that are continuous within elements and discontinuous at element boundaries. Although DG methods have
been invented in the early 1970s. They are very attractive for flow and transport problems in porous media since they can be used to solve hyperbolic
as well as elliptic/parabolic problems, (potentially) offer high-order convergence combined with local mass balance and can be applied to unstructured,
non-matching grids. We present a discontinuous Galerkin method based on
the non-symmetric interior penalty formulation introduced by Wheeler and
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Rivière for an elliptic equation coupled to a nonlinear parabolic/hyperbolic
equation. The equations cover models for groundwater flow and solute transport as well as two-phase flow in porous media. We show that the method
is comparable in efficiency with the mixed finite element method for elliptic
problems with discontinuous coefficients. In the case of two-phase flow the
method can outperform standard finite volume schemes by a factor of ten for
a five-spot problem and also for problems with dominating capillary pressure.
ELLAM methods are space-time Petrov-Galerkin methods where test functions are constant along the characteristics. Numerical integration of certain terms in the bilinear with forward tracking of integration points results
in a mass conservative method that is especially suited for the solution of
convection-dominated transport problems in highly heterogeneous media.
Numerical Parameter Identification in Multiphase Flow through Porous
Media
S.B. Hazra (University of Trier), V. Schulz (University of Trier)
Monday, 17:00–17:30, Hall 5
In this talk we discuss a method of solving inverse problems in non-isothermal
multiphase multicomponent flow through porous media. The conceptual
model is described by a system of nonlinear PDE’s involving unknown parameters.These parameters are to be determined using a set of observations
at discrete points in space and time by an optimization method. It is based
on reduced Gauss-Newton iteration in combination with an efficient gradient
computation. A sensitivity analysis is carried out for the optimum parameter
set. Some numerical results will be presented.
Minisymposium: Simulation-based optimization in industry
H.P. Stehouwer (CQM bv, Eindhoven), L.T. Driessen (Centre for
Quantitative Methods)
Monday, 15:30–17:30, Hall 7
Ever-increasing pressure on the development time of new products has led
to dramatic changes in the way products and processes are designed. In the
past, design practices were based on experimentation using physical prototypes. In the last decade, physical computer simulation models such as circuit
design tools and finite element analysis models have become widely used in
engineering design and analysis. The reliability of these tools has enabled
the virtual prototyping of today’s products. However, designers still face the
problem of choosing an optimal design that fits the design requirements.
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This mini-symposium addresses the situation where finding optimal design parameter settings in situations where expensive and time consuming
computer simulations are used to evaluate product or process characteristics. To explore the design space, designers more and more use dedicated
techniques from statistics and mathematical optimization. The central idea
in most approaches is the creation of so-called compact models (also called
meta-models or surrogate models) to replace the time-consuming functions.
These compact models predict the response parameters as a function of the
design parameters and can be exploited in the optimization. The hardness of
the problem is determined by the presence of non-linearities, the number of
design variables, and the running times of function evaluations.
In this mini-symposium we will invite speakers form industry to talk about
their experiences with dedicated simulation-based optimization techniques.
Optimisation of a stamping process using FEM simulations
E.H. Atzema (Corus Research, Development & Technology)
Monday, 15:30–16:00, Hall 7
Corus is an international metals group providing steel and aluminium solutions to customers worldwide. For Corus automotive is an important market.
Several automotive customers are having problems with body sides tearing in
the corner during the forming process, being stamping. The problems were
not curable by the usual application of process knowledge and simulation
technology by an experienced engineer. Corus RD&T Automotive Applications was therefore looking to develop a methodology for the design process
of body side stamping resulting in a safe process. For this, Corus started a
design optimisation project in cooperation with CQM. This talk details the
practical implications of this project.
If problems occur during (start of) production usually the geometry of the
end product has already been fixed. What can be influenced, however, are socalled drawbeads, the shape of apertures in the blank, and material properties.
Drawbeads restrain the material flow and thus control the drawing process;
they are not part of the end product. The initial size of the aperture cut-out
also influences the sheet metal forming process. It defines the size of the
flange at the inside of the body side under consideration. The material used
was already the best formable grade.
The following six design parameters will be varied:
• Drawbead restraining force on two drawbead segments: in the corner
and elsewhere independently (2 variables)
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• Hole cutout: two points span a bezier curve in the original flat blank
(2*2 coordinates). Outside the design area (i.e. problem area) the current cut out is kept and the curve is tangential to that in two fixed points.
An additional design restriction is that the cutout should not position the sheet
outside of the drawbead, because that renders it disfunctional. Response parameters involved are tearing and strain homogeneity.
COMPACT-CO: an integral meta-modeling approach
E.D. Stinstra (CQM bv, Eindhoven), H.P. Stehouwer (CQM bv)
Monday, 16:00–16:30, Hall 7
In the last decade, virtual prototyping techniques like CAD and CAE have
become widely adopted in product and process design. This has led to a large
interest from industry in efficient techniques for design space exploration and
optimization. One of the most popular approaches is DACE, which stands for
Design and Analysis of Computer Experiments and involves the following
steps:
• Input/output definition: design parameters, response parameters, and
constraints.
• Creation of a simulation scheme.
• Performing of computer simulations, gathering and screening of results.
• Creation and validation of meta-models (e.g., RSM, Kriging) for all
quality characteristics.
• Fast optimization and robust design using meta-models.
Many industrial design optimization problems involve a large number of parameters. An often-heard drawback of the DACE approach is that when the
number of design parameters grows, one may run into what is called the
‘curse of dimensionality’. This talk presents an approach developed by CQM
which enables collaborative optimization of complex products by decomposing the problem at system level and applying DACE at subsystems. This
approach is called Compact-CO and is briefly described below.
The approach starts with carefully mapping the problem structure, which
is represented as a graph with nodes and directed arcs as follows:
• Black-box nodes representing time-consuming analysis models like
FEM or CFD. Incoming arcs denote design parameters and outgoing
arcs model quality characteristics, called response parameters.
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• White-box nodes modeling explicit relations, for instance the average
of a number of node inputs.
DACE is applied to every black-box node in the graph. The resulting metamodels are connected according to the system level graph. This leads to a
system of equations that needs to be solved when the model is predicted.
Since meta-model function evaluations are relatively cheap, powerful techniques like Non-Linear Programming (NLP) and Monte-Carlo analysis can
be directly applied.
Simulation-based optimisation in the semiconductor industry
J.H.J. Janssen (Philips Semiconductors)
Monday, 16:30–17:00, Hall 7
The first study will focus on the development of reliable Response Surface
Models (RSM) for the packaging process of a typical electronic device. The
major objective is to optimise the product/process designs against the possible failure mode of vertical die crack. Finite Element Method (FEM) based
physics of failure models are developed and the reliability of the predicted
stress levels was verified by experiments. In the development of reliable
thermo-mechanical simulation models, both the process (time and temperature) dependent material non-linearity and geometric non-linearity are taken
into account. Afterwards, RSM’s are constructed which cover the whole specified geometric design spaces. Finally, these RSM’s are used to predict, evaluate, optimise and eventually qualify the thermo-mechanical behaviour of
this electronic package against the actual design requirements prior to major
physical prototyping and manufacturing investments.
The second study will focus on the thermal characteristics of an IC package. Until a few years ago thermal data of IC package were reported as a single value thermal resistance. However, these thermal resistances were only
applicable for the environment in which they were measured or modelled.
With the increase in power densities and complexity the need for more accurate models of IC packages became key. Nowadays, so-called Compact
Thermal Models (CTM) are available which describe the thermal behaviour
in steady state as well in the transient domain, very accurately. These CTM’s
are constructed with resistance and capacitance. The values of the components are determined by an optimisation process and is done with dedicated
software. The process of creating these CTM’s will be described and some
examples on how to use them will be given.
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Robust CRT shadow mask optimization using COMPACT-CO
J.W.J.M. van der Heijden (LG. Philips Displays)
Monday, 17:00–17:30, Hall 7
In this presentation, we discuss a project carried out at LG. Philips Displays in
Eindhoven, the Netherlands, where cathode ray tubes (CRTs) are designed. In
our system design phase, several part design groups work together to translate
system level specs to part level specs. Typical for this phase is the use of
CAD/CAE tools for virtual prototyping of parts in combination with design
optimization techniques like response surface modeling to search for feasible
and optimal designs. Current practice is that these design tools are mainly
used at part level.
One of these parts is the so-called shadow mask: a curved metal plate with
some 500,000 holes. Its function is to ensure that the each of the three electron beams can only hit its own color phosphor. For proper functioning, the
mask holes have to fulfill some tight constraints that are position dependent.
Further, the whole mask has to be mechanically stable: able to withstand
shocks and insensitive to vibrations. The challenge is not only to determine
the mask hole geometries in such a way that all constraints are satisfied, but
to determine the geometries that lead to the most robust design, defined as the
maximum value of some objective function minus 3 times sigma.
Response surface models (4) were made describing effective local material
properties. A separate response surface model describes the effect of these
local material properties on overall performance. We used Compact-CO to
combine these five models and to determine the optimal performance. The
most robust optimum could be determined with Compact-CO as well.
The mask hole geometry optimization with Compact-CO proposed different parameter settings as we were used to. It enabled us to maintain performance at reduced costs, leading to substantial cost savings. Further benefits
of this approach will be indicated as well.
On a Constrained Nonlinear Optimization Problem for Preventing Hot
Cracking in Laser Beam Welding
V. Petzet (University of Bayreuth), C. Büskens (University of Bayreuth),
A. Prikhodovsky (New Materials Bayreuth GmbH), V. Karkhin (New
Materials Bayreuth GmbH), H.J. Pesch (University of Bayreuth)
Monday, 15:30–15:50, Hall 14
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Hot cracking is one of the big problems in modern welding techniques, e.g.
in laser beam welding. A new method called multi-beam welding can avoid
or reduce this undesirable effect. Hereby two additional laser beams impose
additional heat sources on the material and thus additional tensile stresses to
compensate for the strain induced by the main laser beam. The aim is to
determine position, size and power of the additional laser beams in order to
minimize the hot cracking.
Form a physical point of view this means that the opening displacement has
to be minimized. In this context the calculation of the temperature field need
to be known.
For the beginning the mathematical model which gives the temperature field
for a fixed time in the weld takes only the heat conduction into account. This
leads to an inhomogeneous elliptic partial differential equation which can be
solved analytically if no boundary conditions are prescribed. In order to fulfil
the boundary conditions describing the finiteness of the weld, the method
of images is used. The hot cracking can then be minimized by solving a
constrained nonlinear optimization problem.
Defects in Object Detection by the Cone Beam Tomography Method in
the Presence of Noise
O.E. Trofimov (SB of Russian Academy of Sciences), E.V. Shaposhnikova (SB of Russian Academy of Sciences)
Monday, 15:50–16:10, Hall 14
Unlike the classic tomography which uses the 2D reconstruction methods
to reconstruct the object inner structure, in the cone-beam tomography the
3D object is reconstructed from its 2D projections. The source data are the
values on a film or a 2D detector array, which are obtained from different
positions of the radiation source moving discretely along some 3D trajectory.
This scheme corresponds to the mathematical problem of three-variable function determination from its line integrals lying in 3D space. Basic methods
of this problem solving are proposed in the papers [1-4]. In this paper the
computer simulation results of the defect size determination are presented in
the presence of noise. The best and the worst directions when reconstructing the density of object are found. For the reconstruction algorithm creation
we used the inversion formula given in [2]. In the paper some connections
and relations between methods given in the papers [1-4] are considered. This
work was supported by the Russian Foundation for Basic Research (projects
03-01-00910, 03-07-09060), and by the Human Capital Foundation.
[1] P. Grangeat, Analyse d’une systeme d’imagerie 3D par reconstruction a partir de
radiographies X en geomwtrie conique. These de doctorat, Grenoble, 1987.
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[2] M. Lavrentiev, S.M. Zerkal, O.E. Trofimov, Computer Modeling in Tomography
and Ill-Posed Problems, VSP (The Netherlands), 2001, 128 pp.
[3] D. Smith, Image reconstruction from cone-beam projections: necessary and sufficient conditions and reconstruction methods. IEEE Trans. Med. Image. MI-4,
1985. PP.14-28.
[4] Trofimov, Cone beam reconstruction and Fourier transform of distributions. Lecture Notes in Computer Science, N 719, pp. 564-571, 1993, Springer-Verlag.
[5] Tuy, An inversion formula for cone-beam reconstruction. SIAM. J. APPL.
MATH. 1983, vol.43, No. 3, PP.546-552.
A Stabilized Chebyshev -Spectral Approach for a Class of Nonlinear OrrSommerfeld Eigenvalue Problems
I. Gheorghiu (“T. Popoviciu” Institute, Cluj-Napoca)
Monday, 16:10–16:30, Hall 14
We investigate the hydrodynamic stability of a thin liquid film flowing down
an inclined plane and sheared simultaneously by a uniform stress. The stress
is due to surface tension gradients and acts on the free boundary of the film.
The competition between gravity and shear stress sets up a steady shear flow
which is a sum of a Poiseuille and a Couette flow, the latter being multiplied
by a factor which contains the relative contribution of superficial and gravitational forces. The natural question is why should the features of the stability
of these two fundamental flows disappear so completely when a free surface
is present?
Clarification of this leads, in linear approximation, to some Orr-Sommerfeld
((O-S) for short) boundary eigenvalue problems with boundary conditions depending nonlinearly on the spectral parameter. For long waves, the critical
Reynolds number is determined by asymptotic analysis.
Based on Chebyshev polynomials, we develop a stable and accurate numerical approach that leads to banded matrices and eliminates the spurious
eigenvalues which are omnipresent in the classical approaches. The asymptotic analysis is in fairly good agreement with well-established studies and is
confirmed by our numerical computations as well as by independent ones. To
the best of our knowledge, no result concerning the completness of the eigenfunctions or other analytic properties are available for our (O-S) problem.
We also investigate numerically, the non-normality of the (O-S) type operators, by computing their pseudospectra and maximal growth rates.
Numerical results concerning the left-most eigenvalue in the complex plane
and neutral stability curves for a large set of mechanical and geometrical parameters are carried out. A scenario of transition to turbulence is also suggested.
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Monday Afternoon
Gradient Computations for Optimal Design of Turbine Blades
K. Arens (TU München, Zentrum Mathematik), P. Rentrop (TU München
Zentrum Mathematik), S.O. Stoll (IWRMM)
Monday, 16:30–16:50, Hall 14
In power plants the aerodynamic optimization of turbine blades is crucial for
efficiency considerations. The last blade row of gas turbines shares considerably in the total power output of a plant. Therefore, any improvements of the
energy conversion from gas flow into rotation can be very profitable. In order
to enhance the efficiency of the last blade row, the corresponding transonic
and supersonic flow field must be considered in more detail. The gas flow
through the blade row suffers from the occurrence of shock-waves. These
shock-waves produce high losses of energy and therefore of efficiency. By
optimizing the blade profile shock-waves can nearly be avoided or remarkably reduced in their strengths. The applied efficient optimization algorithms
are based on gradient information.
The fluid-mechanics are modeled by the 2D Euler equations. The profile of
the turbine blade is described by Bézier polynomials, where the coefficients
are used as design variables. This talk will discuss shortly three different approaches to receive the gradient information: i) by finite differences, ii) via
the sensitivity equation, iii) by an adjoint method.
At the end of the talk different shapes of turbine blades are presented, which
have been computed by our industrial partner SIEMENS AG, Dr. U. Wever.
Fast Shape Design for Industrial Components
E.H. Lindner (Johannes Kepler University Linz), G. Haase (Karl-FranzensUniversität), Ch. Rathberger (Pochestr.1)
Monday, 16:50–17:10, Hall 14
We consider minimizing the mass of a frame in an injection moulding machine. This frame has to compensate the forces acting on the mould inside
the machine and has to fulfill certain constraints. The deformation of the
frame with constant thickness is described by the plain stress state equations
for linear elasticity. This direct problem is solved by a finite element method
and an algebraic multigrid solver.
The mass minimization problem leads to a nonlinear constrained minimization problem that we solve by SQP requiring gradients with respect to
the design parameters. Whenever the design parameters change, then also
the shape will change. Generating a new finite element mesh for each single
shape leads to a nondiffereantiable objective. Here we present an approach
where the mesh is deformed elastically accordingly to the modifications of
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the design parameters. Numerical results are promising and show an obvious
reduction of computational efforts compared to older implementations.
A New Model for the Unsteady Expansion and Contraction of a Long
Two-Dimensional Vapour Bubble Confined Between Superheated or
Subcooled Parallel Plates
K. Das (University of Strathclyde, Glasgow), S.K. Wilson (University of
Strathclyde in Glasgow)
Monday, 17:10–17:30, Hall 14
In this talk we construct and analyse a new mathematical model for a
two-dimensional bubble confined between superheated or subcooled parallel plates, whose motion is driven by mass transfer between the liquid and the
vapour.
The new model is similar to that proposed by Wilson, Davis Bankoff [J.
Fluid Mech. 391 1–27 (1999)], but differs from it in one crucial respect,
namely that, unlike the earlier work, it includes significant mass transfer from
and/or to the semi-circular cap regions at the nose of the bubble as well as
from and/or to the thin liquid films attached to the plates.
When both plates are superheated equally the bubble always expands. In
this case there are two possible constant-velocity travelling-wave solutions
for the expansion of the bubble, namely an unstable fast mode and a slow
stable mode. In particular, the numerical calculations show that eventually
the bubble expands either with the constant velocity of the slow mode or
exponentially.
When both plates are subcooled equally the bubble always collapses to zero
length in a finite time. When one plate is subcooled and the other plate is superheated the situation is more complicated. If the magnitude of the subcooling is less than that of the superheating, then if the magnitude of subcooling
is greater than a critical value then a variety of complicated behaviours (including the possibility of an unexpected ‘waiting time’ behaviour) can occur
before the bubble eventually collapses to a finite length in an infinite time,
whereas if it is less than this critical value then the bubble always expands
and eventually does so exponentially. If the magnitude of the subcooling is
greater than that of the superheating, then the bubble always collapses to zero
length in a finite time.
Scattering of sound waves by a spherical poroelastic shell near a planar
boundary
M. Seyyed (Iran University of Science and Technology)
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Monday Afternoon
Monday, 17:30–17:50, Hall 14
An exact analysis for acoustic scattering by a fluid-saturated spherical porous
elastic shell immersed near the of an acoustic halfspace for an arbitrary angle of plane wave incidence is outlined. The novel features of Biot dynamic
model along with the appropriate wave field expansions, the pertinent boundary conditions, the method of images, and the translational addition theorem
for spherical wave functions are employed to develop a closed-form solution
in form of infinite series. The prime objective is to investigate the dynamic
poroelasticity effects on acoustic scattering and its associated field quantities.
The analytical results are illustrated with a numerical example in which a
spherical cellular aluminum foam shell, submerged near the flat boundary of
a water-filled acoustic halfspace, is insonified by a plane wave at oblique incidence. Subsequently, the basic acoustic field quantities such as the scattered
far-field pressure directivity pattern, form function amplitude, and the scattered acoustic intensity distribution are evaluated and discussed. The effects
of incident wave frequency, shell porosity, and its proximity to the interface
are examined
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Tuesday Morning
Tuesday Morning
9:00–10:00
Plenary lecture
Fields, Focusing and Aberration of charged particle beams in Electrostatic
Accelerators (B. Trowbridge) . . . . . . . . . . . . . . . . . . . . . . . .
10:00–10:30
Break and Poster presentations
10:30–12:30
Scientific Computing in Electronics Industry I (E.J.W. ter Maten; theme:
Electronic industry) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Digital linear control theory applied to automatic stepsize control in electrical
circuit simulation (A. Verhoeven) . . . . . . . . . . . . . . . . . . . . . .
On Nonlinear Iteration Methods for DC Analysis of Industrial Circuits (M.
Honkala) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multidimensional Techniques for Simulating Frequency Modulated Signals
(R. Pulch) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PDAE modelling in network analysis: some experiences with industryrelated research in Germany (M. Günther) . . . . . . . . . . . . . . . . .
Mathematical models in oil transport and processing (A. Fasano; theme:
Chemical technology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Mathematical models for mass transport in non-isothermal saturated or partially saturated waxy crude oils (A. Fasano) . . . . . . . . . . . . . . . .
Mathematical modelling of wax deposition in the turbulent flow of a waxy
crude oil (L. Fusi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Blowdown of hydrocarbons pressure vessels; a compositional approach. (A.
Speranza) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiphase Issues in Design Practice (A. Terenzi) . . . . . . . . . . . . . .
Mathematical models for laser material processing (M.J.H. Anthonissen;
theme: Materials) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modelling, simulation and control issues in laser-induced thermotherapy (D.
Hömberg) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical simulation of laser surface remelting (M.J.H. Anthonissen) . . . .
Solidification of a high-Reynolds-number flow in laser percussion drilling
(W.R. Smith) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation and optimisation of the laser surface hardening of steel (W. Weiss)
Modelling and Characterization in Geophysical Applications (M. Kindelan; theme: Geophysics) . . . . . . . . . . . . . . . . . . . . . . . . . . .
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A Review of the Most Common Reservoir Model Construction Processes.
Uncertainty Quantification (C. Montes) . . . . . . . . . . . . . . . . . . .
Reservoir simulation using the streamline method: Alternatives to minimize
numerical diffusion (P. González) . . . . . . . . . . . . . . . . . . . . . .
Reservoir Characterization Using a Propagation-Backpropagation Method
(M. Moscoso) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Shape reconstruction in 3D Electromagnetic Induction Tomography using
level sets (O. Dorn) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
How to train industrial mathematicians, I (J. Vladislavleva) . . . . . . . . .
Educating Industrial Mathematicians: Some thoughts on aims, circumstances and requirements (J. Wessels) . . . . . . . . . . . . . . . . . . . .
OOWI: Bridging the Gap (E.M. Jordaan) . . . . . . . . . . . . . . . . . . .
The Ideal Industrial Mathematician (J.N. Driessen) . . . . . . . . . . . . . .
How does Mathematics in Industry fit into the European Commission’s
plans? (H. Ockendon) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
How training in Industrial Mathematics can make a difference (H. Holden) .
How can we make the EU take notice of Mathematics? (H. Neunzert) . . . .
The NETIAM Project (R.A. Leese) . . . . . . . . . . . . . . . . . . . . . .
Roots-finding of polynomials (P. Sargolzaei) . . . . . . . . . . . . . . . . .
Artificial Neural Networks: Ways of Its Application in Applied Science and
in Industry (V. Abrukov) . . . . . . . . . . . . . . . . . . . . . . . . . .
Determination of the Phase of a Transfer Function: Theory versus Practice
(P. Sourdille) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A mathematical model for the dynamics of towed pipeline bundles. (N.W.
Manson) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pattern formation and hysteresis in low temperature plasmas (D. Mackey) . .
Beams on inhomogeneous foundation (V. Zoller) . . . . . . . . . . . . . . .
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Fields, Focusing and Aberration of charged particle beams in
Electrostatic Accelerators
B. Trowbridge (Vector Fields Ltd)
Tuesday, 9:00–10:00, Blauwe Zaal
Design software for solving field problems is an essential tool for science
and industry. Such codes are used in a very broad range of applications
which have proved very successful. This presentation will highlight some
these areas and in particular outline some recent work on the topic of small
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electrostatic particle accelerators (such as Van de Graaffs) and DC machines
(Cockcroft-Walton sets) that are used in basic research, material modification, ion implantation and analysis, including carbon dating. The quality of
the beam on target is critical to all these applications. It depends on the characteristics of the ion source and on the optical elements through which the
beam passes. The most critical of these is the accelerator tube. The effectiveness of software packages to model the electrostatic field distributions
in planar and axi-symmetric geometries and to calculate beam trajectories is
discussed with the object of determining the mesh size and precision necessary to obtain reliable predictions of aberration and beam emittance growth.
The computational challenge is to calculate the fields to such accuracies that
sufficiently smooth values of higher derivatives can be obtained in order to
evaluate aberration integrals. The use of an analytic expression fitted to the
numerical results enables third order ray tracing to be compared with general
ray tracing to aid confidence in the numerical finite element solutions. The
field distributions and particle trajectories deep in the interior of such a tube,
where any variation in field is due exclusively to the finite thickness of the
electrodes, have also been calculated. Finally the effect on the beam of the
transverse electric fields introduced into high voltage tubes to suppress secondary particles and reduce bremsstrahlung, the high energy X-rays released
when electrons are slowed down in absorbers has been treated using three
dimensional finite element models.
Minisymposium: Scientific Computing in Electronics Industry I
E.J.W. ter Maten (Philips Research Laboratories Eindhoven)
Tuesday, 10:30–12:30, Hall 11
The ECMI Special Interest Group on Scientific Computing in Electronics Industry has been founded to provide a framework for collaboration between
numerical mathematical scientists and engineers in electronics. Within this
framework the mathematical modeling and the numerical simulation of problems arising in electronics industry are discussed. The minisymposia at ECMI
are meant to present the state of the art approaches from research that is
performed at or done for electronics industry. In the current cases these
are Philips Electronics, Infineon Technologies AG, Aplac Solutions, Nokia,
Magma Design Automation, NEC Electronics and Elpida (NEC/Hitachi).
Topics include: model reduction, control theory techniques for transient simulation, dynamic iteration, multirate time integration, iterative methods for
nonlinear problems, preconditiones for parallel iterative solvers, oscillator
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problems, simulation of multiple frequency modulated radio frequency problems, and optimization.
Digital linear control theory applied to automatic stepsize control in electrical circuit simulation
A. Verhoeven (Technische Universiteit Eindhoven)
Tuesday, 10:30–11:00, Hall 11
Numerical integration methods are used to find the numerical solution of the
transient analysis of electrical circuits. For onestep methods, the local truncation error only depends on the last stepsize, but for multistep methods, this
error is also dependent on the previous stepsizes. Adaptive stepsize control
and order control is used to control these local errors of the numerical solution. For optimization purposes smoother controllers are wanted, such that
the errors and stepsizes also behave smoothly.
For onestep methods, the stepsize control process can be viewed as a digital linear control system for the logarithms of the errors and steps. From a
control-theoretic point of view, the goal is to keep the error close to a reference level by means of the stepsizes. For the BDF-method, which is a multistep method, this control process can only be approximated by such linear
control system. If the stepsize control process is correctly modelled, a finite
order digital linear controller can be designed. This design depends on the
poles of the closed loop dynamics, the adaptivity and the filter orders.
On Nonlinear Iteration Methods for DC Analysis of Industrial Circuits
M. Honkala (Helsinki University of Technology), J. Roos (Helsinki University of Technology), V. Karanko (Helsinki University of Technology)
Tuesday, 11:00–11:30, Hall 11
Modern electronic circuits are typically large, consisting of thousands of transistors and other components. For the simulation of these large, nonlinear
circuits, efficient iteration methods are needed. Choosing the nonlinear iteration method for circuit simulator, we have to take into account the special
properties of both the circuit equations and the circuit simulator, in our case,
APLAC.
The DC analysis of APLAC is based on the (modified) Newton–Raphson
method. It has fast local convergence, but especially in cases where the initial guess for the nonlinear iteration is poor, Newton–Raphson iteration may
diverge or the convergence may be extremely slow. Usually, other methods
with strong convergence properties (e.g., homotopy methods) are slow, while
faster methods (e.g., methods that approximate the inverse of the Jacobian
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matrix) have convergence problems. Therefore, one has to compromise between speed and reliable convergence.
Our goal is to find a method or a combination of methods that converges
robustly enough for badly scaled DC analysis and is also reasonably fast.
In APLAC, transistors and other nonlinear components are modeled such
that the current functions and their first derivatives are available. Therefore,
the Jacobian matrix and the gradient are easy to obtain, but, e.g., the construction of the Hessian matrix would need expensive numerical computation. In
addition, the Jacobian matrices are sparse and often nearly singular.
We concentrate on some trust-region and tensor methods, which should be
efficient in the case of (nearly) singular Jacobian matrices and do not need the
computation of Hessian matrices. We also improve their convergence using
nonmonotone strategy and compare their efficiency to Newton–Raphson and
some conjugate gradient methods. All the methods have been implemented
using the Matlab–APLAC-interface in APLAC. Simulations with relevant industrial circuits are presented.
This presentation is given by J. Roos.
Multidimensional Techniques for Simulating Frequency Modulated Signals
R. Pulch (Bergische Universität Wuppertal)
Tuesday, 11:30–12:00, Hall 11
In communication electronics, many circuits produce oscillatory signals including widely separated time scales. For example, oscillations of a high
frequency may show a slow modulation of amplitude or frequency. Thus
simulating an ODE model of the circuit becomes expensive, since the fast
oscillations restrict the time steps. A multidimensional model yields an alternative strategy for frequency modulated signals by decoupling the time scales.
Consequently, the ODE model transforms into a multirate PDE model. The
efficiency of such a PDE technique depends on the determination of appropriate local frequencies. In the talk, the physical meaning of these frequencies
will be discussed. Thereby, the crucial point is to compare the PDE to a
family of autonomous ODEs including a parameter. Accordingly, additional
conditions are presented, which shall select the desired local frequency function. This analysis is closely related to the information transport in the PDE
system, which allows the use of a method of characteristics. Test results clarify the application of the PDE model in electric circuit simulation. A physical
interpretation of the arising solutions is given.
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PDAE modelling in network analysis: some experiences with industryrelated research in Germany
M. Günther (Bergische Universität Wuppertal)
Tuesday, 12:00–12:30, Hall 11
Partial differential-algebraic equations, for short PDAEs, are frequently used
to incorporate parastic behaviour into electrical network modelling or to
link network equations with multi-physical effects. This modelling approach arises serious questions concerning model validation, analysis (wellposedness and sensitivity), efficient numerical discretization (multiscale behaviour) and implementation (co-simulation and distributed integration).
In this talk we will inspect various examples from electro-thermal, electromagnetic and electro-device interaction that have been investigited within a
joint research project supported by the BMBF (German Federal Minsitry of
Education and Research) in cooperation with Infineon Technologies Munich.
We will point out advances already achieved in approaching these questions,
and address open problems that require future joint research of applied mathematicians, electrical engineers and physicists from both academia and industry.
Minisymposium: Mathematical models in oil transport and processing
A. Fasano (Universitá di Firenze)
Tuesday, 10:30–12:30, Hall 4
It is well known that the peculiar rheological properties of many mineral oils
may produce remarkable difficulties in modelling for instance pipelining processes. This is true in particular for the so called Waxy Crude Oils (WCO’s),
characterised by a high content of heavy hydrocarbons (denominated with the
generic term of ‘wax’). When temperature is sufficiently low wax crystallizes
and the crystals may entangle to form a gel-like structure, thus influencing
rheology in a relevant way. In addition, the presence of a thermal gradient,
caused e.g. by a cold environment, drives the dissolved wax to the pipe wall
(molecular diffusion) with the consequent formation of a solid deposit, which
in turn interferes with the fluid dynamical problem. In this minisymposium
the general question of mass transport in non-isothermal saturated solutions
will be treated, along with the specific problem of wax deposition during
WCO’s pipelining. Another important process that will be dealt with is the
the so-called blowdown in oil phase separators, which consists in producing
a sudden pressure drop in a chamber containing liquid oil and volatile components. Finally some open problems will be proposed. Industrial partners:
EniTecnologie, Snamprogetti.
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Mathematical models for mass transport in non-isothermal saturated or
partially saturated waxy crude oils
A. Fasano (Universitá di Firenze)
Tuesday, 10:30–11:00, Hall 4
Saturation concentration of a given solute in a given solvent is an increasing
function of temperature. For this reason the presence of a thermal gradient
in a saturated solution induces mass transport by diffusion. The situation
analysed is such that at each point of the solution (when it is saturated) the
solute is in equilibrium with the possibly present segregated mass. Density
is supposed to be practically the same for all components, so that dissolution
or segregation do not produce volume changes and the segregated phase is
a suspension, also subject to diffusion. An additional difficulty, which is
peculiar of waxy crude oils, comes from the fact that once the mass flowing
in the saturated solution reaches the ‘cold spots’ of the boundary it creates
a solid deposit. The thermal field is supposed to be stationary. The model
describes the whole process, including the onset of desaturation, and predicts
the deposition rate. The research is the result of a cooperation between I2T3
and EniTecnologie and is a joint work with S. Correra, L. Fusi, M. Primicerio.
Mathematical modelling of wax deposition in the turbulent flow of a waxy
crude oil
L. Fusi (University of Florence)
Tuesday, 11:00–11:30, Hall 4
In this work we present a mathematical model of wax deposition for a waxy
crude oil flowing in a pipeline in turbulent regime. Due to turbulence, temperature depends only on the longitudinal coordinate except for a thin boundary
layer near the pipe wall, where a radial thermal gradient induces lateral mass
transport of dissolved paraffin and deposition by molecular diffusion. The
thickness of the boundary layer is a fraction of the deposit determined imposing the balance of forces in the turbulent core. The equation for the deposit
front is derived by writing mass balance in a pipe segment. On the basis
of such an equation we formulate a criterion for partitioning the pipeline in
segments in which the deposit thickness can be considered independent of
the longitudinal coordinate. Then we write an iterative scheme that provides
the evolution of the deposit front in each segment. An example of numerical
implementation is given.
The research is the result of a cooperation between I2T3 and EniTecnologie
and is a joint work with S. Correra, A. Fasano and M. Primicerio.
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Blowdown of hydrocarbons pressure vessels; a compositional approach.
A. Speranza (I2T3)
Tuesday, 11:30–12:00, Hall 4
We propose a model for the simulation of the blowdown of vessels containing two-phase (gas-liquid) hydrocarbon fluids, considering non equilibrium
between phases. Two phases may be present either already at the beginning of the blowdown process (for instance in gas-liquid separators) or as
the liquid is formed from flashing of the vapor due to the cooling induced
by pressure decrease. There is experimental evidence that the assumption
of thermodynamic equilibrium is not appropriate, since the two phases show
an independent temperature evolution. Thus, due to the greater heat transfer between the liquidphase with the wall, the wall in contact with the liquid
experiences a stronger cooling than the wall in contact with the gas, during
the depressurization. As a consequence, the vessel should be designed for a
lower temperature than if it was supposed to contain vapor only.
Our model is based on a compositional approach, and it takes into account
internal heat and mass transfer processes, as well as heat transfer with the
vessel wall and the external environment.
Numerical simulations show a generally good agreement with experimental measurements.
Multiphase Issues in Design Practice
A. Terenzi (Snamprogetti)
Tuesday, 12:00–12:30, Hall 4
Oil and gas upstream facilities designers are concerned with lack of knowledge on multiphase flow problems. Some related topics are mentioned below:
• Phase Distribution in T-Junctions: exhaustive modelling of the flow
distribution through T-junctions, giving indication of the influence of
parameters as flow rate, flow regime, pressure, on splitting properties,
does not exist, causing difficulties in designing complex piping systems
of treatment plants;
• Slug Size Prediction: slug flow regime is the most difficult to handle,
since it cannot be considered as steady even if it is stabilized, and receiving facilities must be properly sized to contain liquid slugs. However, the uncertainty on slug size calculation is great (100 % error),
even for the up-to-date commercial codes;
• Thermal Sizing of Vessels and Separators: the low temperature limit of
vessels and separators thermal sizing is defined by blowdown simulations. Commercial codes usually assume thermodynamic equilibrium,
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if two-phase fluids are present. But experiments show that the assumption of thermodynamic equilibrium is inaccurate, since the two phases
show an independent temperature evolution. Thus, due to stronger
cooling of the wall in contact with the liquid, the vessel should be designed for lower temperature than if it would contain vapor only.
• Hydrate Formation in Pipelines : hydrates are solids resembling ice
in appearance, which consist of gas molecules surrounded by cages of
water molecules. The formation of hydrates in oil and gas pipelines
represent a serious problem. Their formation usually occurs in seasonally cold or sub-sea environments with low temperatures and high
pressure. In particular, hydrate blockages becomes a real menace to
flow assurance in inadequately protected flowlines.
Scope of this note is to stimulate discussion and research on the above subjects, in order to collect new ideas for possible development of new reliable
simulation tools aiding design activities.
Minisymposium: Mathematical models for laser material processing
M.J.H. Anthonissen (Technische Universiteit Eindhoven), D. Hoemberg
(Weierstrass Institute)
Tuesday, 10:30–12:30, Hall 12
Since its first demonstrations in 1960, the laser (light amplification by stimulated emission of radiation) found its use in a variety of industrial applications. The reason is that lasers typically produce energy in a highly concentrated area and that the energy is transferred without direct contact. The goal
of this minisymposium is to present different laser applications and to show
how mathematics can contribute to a better performance.
The first talk is concerned with laser surface hardening of steel. Here, the
goal is to produce a hard surface avoiding surface melting. Accordingly the
optimal control of this process will be the dominant part of this presentation.
The second speaker will discuss a model for laser surface remelting, a process to improve the surface quality of steel components. In this talk the emphasis will be put on the efficient numerical simulation using adaptive grids,
which are especially well-suited for problems with moving heat sources.
The third talk is devoted to mathematical modeling of laser drilling, a
method which is used e.g. to drill holes in turbine blades including the study
of radiation, heat transfer and flow of material.
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In the last talk a medical application is presented. In laser thermotherapy
a laser fibre is placed in a cancer tumor, then the tumor tissue is heated until
it is coagulated and thus destroyed. The focus in this talk is on mathematical
modeling and control for an optimal therapy planning.
Modelling, simulation and control issues in laser-induced thermotherapy
D. Hömberg (Weierstrass Institute for Applied Analysis)
Tuesday, 10:30–11:00, Hall 12
In a first step towards life sciences applications we have started to apply our
laser hardening model to the case of laser-induced thermotherapy. This is a
cancer therapy in which laser light is guided through a transparent catheter
into a tumor. The absorbed light leads to a heating of the tissue. In contrast
to hyperthermia cancer treatments where the temperature does not exceed
43 o C, say, in this process the tissue is heated up to more than 60 o C leading
to a coagulation of the tumor tissue and thus a destruction of the tumor.
We report on first results in modelling and simulation of the process and
discuss optimal control problems related to therapy planning and the design
of applicators.
Numerical simulation of laser surface remelting
M.J.H. Anthonissen (Technische Universiteit Eindhoven)
Tuesday, 11:00–11:30, Hall 12
We consider a model for laser surface remelting, a process to improve the
surface quality of steel components. The mathematical model consists of the
two-dimensional heat equation for temperature as well as a number of ordinary differential equations for volume fractions. The equations are coupled
via the source terms.
In this talk the emphasis will be put on the efficient numerical simulation
using adaptive grids, which are especially well-suited for problems with moving heat sources. To account for the local high activity due to the heat source,
we introduce local uniform grids and couple the solutions on the global coarse
and local fine grids using the local defect correction (LDC) technique.
The LDC method is an inter-grid communication mechanism that allows
solving boundary value problems on a composite grid without explicitly
forming the discretization on the grid. Its strength lies in the ability to use
existing single uniform grid solvers only as this leads to simple data structures, simple accurate discretization stencils, and the ability to use fast solution techniques.
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Solidification of a high-Reynolds-number flow in laser percussion drilling
W.R. Smith (University of Birmingham), R.M.M. Mattheij (Technische
Universiteit Eindhoven)
Tuesday, 11:30–12:00, Hall 12
An extension to the enthalpy method is developed to study the solidification
of a high-Reynolds-number flow moving across a solid surface. This method
is used to investigate the competition between inertia, melting and freezing
for the flow of molten aluminium across a cool solid aluminium surface. The
molten aluminium initially freezes due to rapid thermal conduction into the
solid. Depending on the sensible heat of the molten aluminium, one of two
situations may develop. (i) If the molten aluminium has sufficient sensible
heat, the chill melts back and melting of the original solid follows. The melting is curtailed by the approach of the trailing edge of the fluid. The molten
aluminium then begins to resolidify which terminates abruptly with the passing of the trailing edge of the liquid/gas interface. (ii) If the molten aluminium
has insufficient sensible heat, solidification continues until the passing of the
trailing edge of the liquid/gas interface or the flow is engulfed. The rate of
solidification may be reduced by introducing a decreasing initial velocity profile, but this results in fluid clumping. The results are interpreted in terms of
the recast and bellow shape observed during laser percussion drilling.
Simulation and optimisation of the laser surface hardening of steel
W. Weiss (Weierstrass Institute for Applied Analysis)
Tuesday, 12:00–12:30, Hall 12
We discuss control strategies for the surface hardening of steel with laser or
electron beam. The goal is to achieve a prescribed hardening depth avoiding
surface melting. Our mathematical model consists of a system of ODEs for
the phase volume fractions coupled with the heat equation. The system is
solved semi-implicitly using the finite element method.
To obtain a uniform hardening depth we apply a PID feedback control. We
present results by controlling the temperature on and below the surface and
derive a strategy in order to achieve a uniform hardening depth. Thereby we
can compute an optimal (not constant) surface temperature in the hot spot,
which has to be adjusted by the machine process control.
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Minisymposium: Modelling and Characterization in Geophysical
Applications
M. Kindelan (Universidad Carlos III de Madrid)
Tuesday, 10:30–12:30, Hall 13
Geophysical applications constitute an important source of challenging mathematical problems which often result in the development of new algorithms
and techniques with broad applicability. The objective of this minisymposium is to present new contributions to this area, both from the point of view
of modelling (direct problem) and characterization (inverse problem).
Of particular interest, due to its economic relevance, is the problem of simulation and characterization of oil reservoirs. The petroleum engineer uses
these simulators in order to design an efficient production strategy. The paper by Guillermo Montes (Repsol-YPF) will present the point of view of the
industry regarding the use of reservoir modelling and characterization techniques and what are the present limitations and challenges.
New applications require very efficient reservoir simulation programs. In
this context, streamline methods have become increasingly popular because
of their ability to perform rapid flow simulations of high-resolution models.
The key idea is to decouple the flow and transport calculations through the
introduction of streamlines. The paper by Pedro González will describe the
streamline method and will present some techniques to eliminate the undesirable numerical dissipation of the method.
Although the reservoir engineer can use very accurate simulators, the lack
of information about the porous media itself often prevents a good matching between model results and experimental data. Reservoir characterization
refers to the identification of reservoir parameters (permeability, porosity, ?)
from production data. The paper by Miguel Moscoso will describe an efficient adjoint inverse method technique to automate this history matching
process.
Finally, Oliver Dorn will present a new level sets based inversion algorithm
for 3D Electromagnetic Induction Tomography (EMIT), which is a new imaging tool which can be used for a variety of geophysical and environmental
monitoring problems.
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A Review of the Most Common Reservoir Model Construction Processes.
Uncertainty Quantification
C. Montes (REPSOL-YPF)
Tuesday, 10:30–11:00, Hall 13
Oil and gas reservoir model construction is mainly a database and study propose dependent process. Hence several workflows have been standardized
in the oil industry as a guide to complete models successfully. The whole
model construction chains integrate several sub-models from the first structural model to the very final dynamic model. The integration process of all
these sub-models should be such one that a consistent final model can be
achieved. In each step several methodologies are available for the geoscientist everyone having its own benefits, constrains and limitations. Even though
a high consistency model is reached at the end of the process, still the initial database quality and quantity will confer an implicit uncertainty on the
results. One of the most important and at the same time most difficult issues to quantify regarding a reservoir model is the uncertainty assessment
process that should be included together with the final simulation model. A
review of the most common work flows, methodologies, integration process
and uncertainty quantification techniques will be fulfilled during the conference by highlighting the most important research gaps and improvement requirements.
Reservoir simulation using the streamline method: Alternatives to minimize numerical diffusion
P. González (Universidad Carlos III de Madrid), M.K. Kindelan (Universidad Carlos III)
Tuesday, 11:00–11:30, Hall 13
Due to the evolution in computer science nowadays it is possible to treat with
large reservoir models with fairly good accuracy. In this context it is usual
to work with models of millions of cells that are very time consuming if they
are solved with the traditional finite difference methods. This leads to the developing of numerical methods that can handle these huge models efficiently
saving as much time as possible. Among all these methods the streamline
method has become very popular due to its high speed.
The key point of the streamline method is that it decouples the flow and
transport calculations through the use of streamlines, transforming the transport equation in two or three dimensions into many one-dimensional transport
equations which can be solved much faster. The method is best suited for convection dominated flows. Other effects such as compressibility or capillary
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pressure can not be solved along the streamlines, and therefore finite differences have to be used to handle them.
The speed of the method is only limited by the need to project the saturation distribution over the streamline to the finite difference grid in order to
calculate the coefficients of the pressure equation. This projection produces
considerable numerical dissipation, making the method less accurate.
In this paper, we compare different algorithms to integrate the streamline
hyperbolic equation along the streamlines (upwind, front-tracking) and different alternatives to project the results from the streamlines to the grid in
order to minimize numerical diffusion.
Reservoir Characterization Using a Propagation-Backpropagation Method
M. Moscoso (Universidad Carlos III de Madrid)
Tuesday, 11:30–12:00, Hall 13
Nowadays, reservoir characterization is a crucial aspect of any optimal reservoir management strategy. In this problem, one tipically estimates model
parameters, such as the permeability or porosity distributions, from the production data recorded at the wells (oil flow, water flow, transient pressure response, ...). Since the flow within the reservoir depends on many unknowns,
the engineer uses some estimations in his model and compares the results of
the simulator with the data avalaible. By an iterative procedure he tries to
minimize the errors between the simulations and the real data. This amounts
to the solution of an inverse problem. Usually, the inverse problem is solved
through the sensitivity coefficients. However, sensitivity coefficients need to
be computed at each cell of the reservoir grid and at each time, and therefore
this procedure can be computationally prohibitive for fine-scale reservoirs.
We will estimate the permeability distribution of the reservoir by means
of a propagation-backpropagation method. This is an efficient method for
solving inverse problems that do not require the computation of the sensitivity coefficients. Since the inverse problem is ill-posed we will present some
regularization techniques too.
We will consider the case of secondary recovery, where water is injected in
some wells in order to enhance oil production. We will use a simplification of
the Black-oil model, which considers two incompressible phases (water and
oil) in a porous medium, neglecting gravity effects and capillary pressure.
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Shape reconstruction in 3D Electromagnetic Induction Tomography using level sets
O. Dorn (Universidad Carlos III de Madrid)
Tuesday, 12:00–12:30, Hall 13
Electromagnetic Induction Tomography (EMIT) is an interesting and promising new imaging tool which can be used for a variety of geophysical and environmental monitoring problems, for example for the monitoring of pollutant
plumes in or above the ground water table or for finding mineral deposits in
the earth. It uses very low-frequency electromagnetic waves (about 1 kHz
or less). The advantage of these low frequency waves is that they can penetrate sufficiently deep into the earth to reach the interesting regions. However,
the resulting mathematical inverse problem is inherently three-dimensional,
large-scale, highly nonlinear and extremely ill-posed. We present a novel inversion algorithm for 3D EMIT which tries to overcome these difficulties by
formulating the inverse problem as a shape reconstruction problem. Since
the number and topologies of the shapes are a priori unknown, a powerful
tool needs to be used for modelling and propagating these shapes during the
inversion process. We have chosen to use a level set representation for this
purpose. We will present in the talk numerical results of this new 3D inversion algorithm from synthetically created data for realistic model problems,
and will discuss the advantages and limitations of this method.
Minisymposium: How to train industrial mathematicians, I
J. Vladislavleva (Technische Universiteit Eindhoven)
Tuesday, 10:30–12:00, Hall 5
The post-graduate program Mathematics for Industry at the Technische Universiteit Eindhoven organizes a minisymposium titled: “How to train industrial mathematicians.”
The goal is to collect view points of people from science, industry, and training programs on the following subjects:
• What is the demand for “industrial mathematicians” at the moment?
• How to select and educate students to become industrial mathematicians?
• What is the philosophy of programs with aforementioned objective?
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• What is the appropriate ratio between gaining knowledge and gaining
skills?
Both the Mathematics for Industry program and the ECMI educational circuit
will benefit from this minisymposium since the questions addressing the vital
decisions that have to be made at every educational program will be posed
and discussed.
In this first part of our minisymposium four speakers are scheduled. They
will talk about their ideas on the issue of training industrial mathematicians,
based on their own experiences in this field; as director of the Mathematics for
Industry-program, as group leader of an R&D-department, as problem owner
or as a former trainee of Mathematics for Industry.
This part can be attended independently from the second part. For more
information, contact:
Catherine Vladislavleva
Bertil van Zweeden
Cornè Botha
Tanya Barysenka
e-mail:
e-mail:
e-mail:
e-mail:
[email protected]
[email protected]
[email protected]
[email protected]
Educating Industrial Mathematicians: Some thoughts on aims, circumstances and requirements
J. Wessels (EURANDOM)
Tuesday, 10:30–11:00, Hall 5
In the presentation some thoughts will be developed about the role of mathematicians in industry. It will also be indicated under which circumstances
the industrial mathematician operates. Role and circumstances determine the
requirements which have to be fulfilled by the industrial mathematician. It
should be the main aim of an academic program on industrial mathematics to
produce mathematicians who fulfill the requirements.
Some theses that will be defended are:
• The primary role of industrial mathematicians lies in innovation processes;
• The industrial mathematician needs some background in the field of
application;
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• For an industrial mathematician it is more important to be able to identify mathematical problems than to be able to solve them;
• Industrial mathematics is just like ordinary mathematics, but practicing
industrial mathematics is not similar to doing research mathematics;
• Good industrial mathematicians are very useful, whereas mediocre industrial mathematicians are completely useless.
OOWI: Bridging the Gap
E.M. Jordaan (Dow Benelux B.V.)
Tuesday, 11:00–11:30, Hall 5
Upon graduation day, many students in mathematical sciences quickly discover that their degrees don’t offer the best career opportunities. Very few
job-adds say: mathematician wanted. These unfortunate students find out
that the industry expect them to be the perfect mixture of expert, innovator,
teacher and salesman. In my talk I will explain how the OOWI-program has
equipped me with the ’necessary and sufficient’ skills to bridge the gap.
The Ideal Industrial Mathematician
J.N. Driessen (Thales Netherlands B.V.)
Tuesday, 11:30–12:00, Hall 5
Based on a sketch of daily life in an industrial environment I will try to outline the contours of the ideal industrial mathematician. Additionally, I will
try to identify those characteristics that can be trained outside an industrial
environment.
Minisymposium: How does Mathematics in Industry fit into the
European Commission’s plans?
H. Ockendon (Oxford University)
Tuesday, 10:30–12:00, Hall 7
This session will provide an opportunity for us to discuss our role within the
EU funding mechanisms. We will compare our experiences and see how we
may be able to affect the future. A number of short talks will be given but the
main part of the minisymposium will be devoted to general discussion.
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How training in Industrial Mathematics can make a difference
H. Holden (Norwegian University of Science and Technology)
Tuesday, 10:30–11:00, Hall 7
Postgraduate Training in Industrial Mathematics gives added-value to a student with a conventional degree in mathematics or computer science. It will
not only prepare them for work in the industrial/commercial sector in Europe
but will also help to forge strong links between industry and universities.
How can we make the EU take notice of Mathematics?
H. Neunzert (Fraunhofer ITWM)
Tuesday, 11:00–11:30, Hall 7
Mathematics is now more than ever needed for a very wide range of applications. Mathematicians are trained to apply their methods in many different
fields by working collaboratively with other scientists. Is it not time that this
was acknowledged by the EC and that a place for mathematics is made in
FP7?
The NETIAM Project
R.A. Leese (Smith Institute)
Tuesday, 11:30–12:00, Hall 7
The NETIAM project (New and Emerging Themes in Industrial and Applied Mathematics) is a support action under the NEST programme (New and
Emerging Science and Technology) within Framework 6. Its objective is to
demonstrate the great untapped potential of mathematics as a foundation for
building adventurous and multidisciplinary research proposals. Instead of the
conventional use of mathematics as a tool for analysis and quantitative modelling in well-specified areas, NETIAM will focus on a much earlier stage
in the process, namely where mathematics can be used as a framework for
the formulation of unexplored research challenges. NETIAM is addressing
in particular the following four themes, cutting across key issues in science,
society and technology: the business environment, criminality in the social
environment, visualization and simulation, and complexity at the molecular
level. The value of NETIAM derives from the breadth of these themes, coupled to their common mathematical underpinnings of multi-scale phenomena,
complexity, risk and uncertainty. This presentation will explain the structure
of the NETIAM project, opportunities for getting involved and the possible
longer-term activities that could result.
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Roots-finding of polynomials
P. Sargolzaei (University of Sistan and Balouchestan), A.R. Mohammay
(University of Sistan and Balou)
Tuesday, 10:30–10:50, Hall 14
Polynomials with multiple zeros appear frequently in practical applications
and most root-finding methods have difficulties with their numerical calculation. Here we study a method to obtain the compansion matrix of the polynomial and the eigenvalue of the compansion matrix which are good approximation to the polynomial roots. The determinetal equation are solved iteratively
by QR algorithm and solved by using Matlab and Maple software. Initial
values choosing conditions for convergency are tabulated.
Artificial Neural Networks: Ways of Its Application in Applied Science
and in Industry
V. Abrukov (Chuvash State University), D.A. Troeshestova (Chuvash
State University), R.I. Pavlov (Chuvash State University), G.I. Malinin (Chuvash State University)
Tuesday, 10:50–11:10, Hall 14
Artificial neural networks (ANN) can be considered as universal tool of approximating of multidimensional functions. A short review of examples of
ANN usage in various fields of science and industry obtained by the authors
of the paper is presented.
1. Results concerning the usage of ANN technique for solving of inverse
problems for optical diagnostic of objects by means of incomplete data about
image or signal. It is very important for optical fiber sensors, smart sensors
and MEMS. It makes possible to use an ANN-like chip (microprocessor) for
automated control systems.
2. Results concerning possibilities of modeling of hydrodynamics phenomena and their forecasting. It was shown that ANN can approximate the wave
shape with a good accuracy. From a practical point of view, the major interest
is the research of a neural network’s feasibility for defining the impact force
and coordinates of impact by means of a wave shape measured at unknown
distance from impact. This task is the inverse problem of tsunami.
3. An ANN models of combustion wave propagation. The new approach to
solution of the task of experimental determination of the profiles of temperature and heat release rate by means of the ANN models and measurement of
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burning rate of combustion wave is represented.
4. An ANN model of deflagration-to-detonation transition under various experiment conditions.
5. An ANN model of automatic control system of boiler unit during transient
processes.
The ANN “Neural Networks Wizard 1.7” - www.basegroup.ru was used by
us for fulfillments of these works. Simulation of socio-economic systems and
systems of education as well as modeling of terrorist threats and systems of
their preventing in frameworks of Global War on Terrorism are the perspective tasks, but demand a very serious work and not solved yet.
Determination of the Phase of a Transfer Function: Theory versus Practice
P. Sourdille (Dublin Institute of Technology), P. Sourdille (Dublin Institute of Technology), A. O’Dwyer (Dublin Institute of Technology)
Tuesday, 11:10–11:30, Hall 14
In control systems, a way to evaluate the stability of a system is to determine
the magnitude and phase of the open loop system transfer function in the
frequency domain. But due to the nature of the phase expression, practice and
theory are not aligned. Some problems arise when the phase is determined,
caused by the properties of the function tan−1 . This paper analyses these
phase problems for a third order lag system and a third order lag with time
delay system. It also presents modifications to obtain the analytically correct
phase values from the computed values.
A mathematical model for the dynamics of towed pipeline bundles.
N.W. Manson (University of Strathclyde, Glasgow), S.K. Wilson (Strathclyde University), B.R. Duffy (Strathclyde University)
Tuesday, 11:30–11:50, Hall 14
In the North Sea offshore oil industry typical pipeline bundles of up to 8 km
length and 1 m diameter consist of a number of petroleum pipelines, control
lines and umbilicals housed in a carrier pipe. They are prefabricated on shore
and towed into position using the so-called Controlled Depth Tow Method
(CDTM), which involves attaching a heavy towhead to the each end of the
bundle and suspending the whole system between two powerful tugboats.
The front tug tows the bundle and the back tug is used to maintain tension
in the bundle and to assist with steering. During the tow, various modes
of oscillation are observed. The tugs’ velocities are continuously adjusted
during the tow so as to control the path of the bundle, to keep it clear of
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the seabed and the free-surface waves, and to avoid excessive tension and
distortion. As the final location is approached the tow speed is reduced and
the bundle is lowered on to the seabed. A typical tow takes two or three days.
In the present work, supported by Subsea 7, Aberdeen, UK via the EPSRC CASE Award Scheme under the auspices of the Faraday Partnership in
Industrial Mathematics coordinated by the Smith Institute, we construct and
analyse a mathematical model for the dynamics of a pipeline bundle being
transported using the CDTM. In the simplest case the model predicts that the
motion comprises a very long wave travelling quickly from the back to the
front of the bundle on a timescale of 30 seconds and a ‘sloshing’ mode with
a period of about 20 minutes. Both of these observations are consistent with
actual observations. The predictions of the model are analysed for a range
of physically relevant parameter values and, in particular, stable and unstable
regions of parameter space are identified.
Pattern formation and hysteresis in low temperature plasmas
D. Mackey (Dublin City University), M.M. Turner (Dublin City University)
Tuesday, 11:50–12:10, Hall 14
A key criterion for the utilisation of inductively coupled plasmas in microelectronics processing or material surface modification is that the plasma be
free of instabilities that produce stationary or slowly varying spatial structures
since these may disastruously affect the quality of the process.
With this objective in mind, a macroscopic model arising in high frequency
plasma discharges with one or two-dimensional geometries is investigated.
This model consists of two coupled nonlinear partial differential equations
(mass and energy balance) and displays a rich dynamical behaviour. This talk
will concentrate on the formation of spatially inhomogeneous patterns (observed experimentally as periodic modulations in the temperature and light
output) and on their dependence on the parameters of power and pressure,
which exhibits bistability and hysteresis.
Beams on inhomogeneous foundation
V. Zoller (Budapest University of Technology and Economics), I. Zobory
(Budapest University of Technology and Economics)
Tuesday, 12:10–12:30, Hall 14
We consider an infinite beam laying on an elastic foundation of varying stiffness/damping parameters given by step functions s(x) and k(x), representing
a railway track and subjected to the action of a damped oscillatory load moving at velocity v.
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The vertical deflection of the rail is governed by PDE
E I ∂x4 z + ρ A ∂t2 z + k(x) ∂t z + s(x)z = Gewt δ(x − vt),
where δ stands for Dirac’s unit impulse distribution and w stands for a complex number. Solution function z(x, t) to the previous equation must satisfy
boundary condition
lim z(x, t) = 0.
|x|→∞
Closed-form solutions to the corresponding boundary value problems are
obtained over each time interval, where the foundation parameters have constant values under the load. The set of these solutions can serve as a base
for building up an effective numerical method for the case of continuously
varying stiffness/damping parameters of the track.
The results are generalizations to the authors’ former paper, treating the
case of a single jump in foundation paramaters, published in:
Railway track dynamics by using Winkler model with initial geometrical
irregularity and stiffness inhomogeneity. In: Zobory, I. (ed) Proc. 8th Mini.
Conf. Vehicle System Dynamics, Identification and Anomalies. Budapest
Univ. Technology Economics (2002), to appear.
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Tuesday Afternoon
13:30–14:30
Plenary lecture
Statistics as a Catalyst for Process and Product Innovation and Improvement (S. Bisgaard) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
14:30–15:30
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Plenary lecture
On the reliability of repairable systems: methods and applications (F. Ruggeri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15:30–16:00
16:00–18:00
Scientific Computing in Electronics Industry II (E.J.W. ter Maten; theme:
Electronic industry) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 H 11
Towards Hierarchical Multirate-Methods In Circuit Simulation (M. Striebel) 91
DRK methods for time-domain oscillator simulation (M.F. Sevat) . . . . . . 91
Reduced order models for eigenvalue problems (J. Rommes) . . . . . . . . . 92
Preconditioners and flexible iterative solvers for the iterative solution of linear systems in circuit simulation (U. Jaekel) . . . . . . . . . . . . . . . . 92
Synthesis and Optimization of an On-Chip Power Grid (S.H.M.J. Houben) . 93
Mathematics of (Portable) Energy Storage Devices (E.A. Verbitskiy; theme:
Chemical technology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 H 4
Mathematical Modelling and Optimization of Rechargeable Batteries (E.A.
Verbitskiy) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
A Detailed Numerical Model for Direct Methanol Fuel Cells (J. Fuhrmann) . 95
Mathematical models and their application in electrochemical reactor design
(J. Deconinck) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
Mathematical modeling of glass 1 (P. Kagan; theme: Materials) . . . . . . . 96 H 12
FPM+radiation=mesh free approach in radiation problems (A. Wawrenczuk) 96
Modeling of the Relevant Processes in the Feeder (F.J. Gonzalez Padilla) . . 97
Modelling the press-blow process of container glass (S.M.A. Allaart-Bruin) . 98
Modeling of glass pressing stage in bottle manufacturing (P. Kagan) . . . . . 98
How to train industrial mathematicians, II (J. Vladislavleva) . . . . . . . . 99 H 5
Title to be announced (M.P. Sørensen) . . . . . . . . . . . . . . . . . . . . . 100
Industrial Mathematics Essentials (S.J.L. van Eijndhoven) . . . . . . . . . . 100
Industrial and Financial Mathematics at EURANDOM (A. Di Bucchianico) 101 H 7
Tuesday Afternoon
A multi-scale approach to functional signature analysis for product end-oflife management (T. Figarella) . . . . . . . . . . . . . . . . . . . . . . .
Theory and Simulation of Lithium-ion Batteries: from single cycle performance to long-term aging effects. (D.L. Danilov) . . . . . . . . . . . . .
Reinsurance of Large Claims (S.A. Ladoucette) . . . . . . . . . . . . . . . .
Contributed presentations (theme: Financial mathematics/Geophysics) . .
Portfolio Analysis in Finance Mathematics (D.S. Hooda) . . . . . . . . . . .
Fuzzy Binary Tree Model for European-Style Vanilla Options (H. Reynaerts)
Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems (K.O.J. Westerlund) . . . . . . . .
Effective Estimation of Banking Liquidity Risk (P.C. Tobin) . . . . . . . . .
Efficient Rank Reduction of Correlation Matrices (I Grubisic) . . . . . . . .
Coupling of open source geochemistry and transport tools for an efficient
geochemistry analysis (A. Dimier) . . . . . . . . . . . . . . . . . . . . .
High Peclet Number Flows in a Slender 3D Lid Driven Cavity: Applications
to Scraped Surface Heat Exchangers (M.E.M. Lee) . . . . . . . . . . . .
Decision Support in Managing Fluids and Systems Applying Constraint
Logic Programming. (J.G.C.M. Goossens) . . . . . . . . . . . . . . . . .
A model for fluid flow in a scraped-surface heat exchanger (S.K. Wilson) . .
New schemes for differential-algebraic stiff systems. (E. Alshina) . . . . . .
Numerical solution of boundary value problems by a method of dynamic
potentials. (A.B. Alshin) . . . . . . . . . . . . . . . . . . . . . . . . . .
A CFL-like Constraint for Fast Marching Level Sets Method (F. Bernal) . . .
On the effect of discontinuous properties of wood chips in the behaviour of
a digester (A. Araújo) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Statistics as a Catalyst for Process and Product Innovation and
Improvement
S. Bisgaard (University of Massachusetts-Amherst)
The context in which statistical process control methods are employed has
changed dramatically over the past few decades. Increasingly networked sensors - thermo couples, pressure gages, flow meters and even video cameras are connected to powerful computers running sophisticated software to monitor complex processes. In this data rich environment, process data are multivariate exhibiting cross correlations and frequently also autocorrelation. In
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this talk we will demonstrate the use of traditional as well as new multivariate
techniques for the control and optimization of complex processes. We will
also discuss how other statistical techniques in general can act as the catalyst
for process and product innovation and improvement.
On the reliability of repairable systems: methods and applications
F. Ruggeri (CNR IMATI, Milano)
Repairable systems subject to minimal repair are those systems whose reliability is the same just before a failure and after the corresponding repair. Failures of such systems are often described by means of non-homogeneous Poisson processes (NHPP). We review the current literature (mainly in a Bayesian
framework), present results on both parametric and nonparametric models
and illustrate them in two industrial applications. The former deals with gas
escapes in a distribution network whereas the latter analyses the failures of
some components in subway trains.
Minisymposium: Scientific Computing in Electronics Industry II
E.J.W. ter Maten (Philips Research Laboratories Eindhoven)
Tuesday, 16:00–18:30, Hall 11
The ECMI Special Interest Group on Scientific Computing in Electronics Industry has been founded to provide a framework for collaboration between
numerical mathematical scientists and engineers in electronics. Within this
framework the mathematical modeling and the numerical simulation of problems arising in electronics industry are discussed. The minisymposia at ECMI
are meant to present the state of the art approaches from research that is
performed at or done for electronics industry. In the current cases these
are Philips Electronics, Infineon Technologies AG, Aplac Solutions, Nokia,
Magma Design Automation, NEC Electronics and Elpida (NEC/Hitachi).
Topics include: model reduction, control theory techniques for transient simulation, dynamic iteration, multirate time integration, iterative methods for
nonlinear problems, preconditiones for parallel iterative solvers, oscillator
problems, simulation of multiple frequency modulated radio frequency problems, and optimization.
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Towards Hierarchical Multirate-Methods In Circuit Simulation
M. Striebel (Bergische Universität Wuppertal)
Tuesday, 16:00–16:30, Hall 11
In full chip design the behaviour of electrical circuits with thousands or even
millions of nodes and transistors has to be verified by means of mathematical simulation. Due to their complexity, large integrated circuits are often
partitioned into subcircuits of different functionality and different transient
behaviour. These subcircuits are modelled independently and composed to
one macro system at last.
To solve the differential algebraic equations (DAE) that originate from applying charge oriented modified nodal analysis (MNA) one can exploit the
varying levels of activity using multirate-methods. These methods integrate
the subsystems with appropriate stepsizes in order to accelerate the process
of simulation.
Based on charge oriented ROW-schemes a multirate-scheme for index-1
DAEs is presented that can deal with an arbirtrary amount of subblocks by
using a hierarchical structure.
DRK methods for time-domain oscillator simulation
M.F. Sevat (Philips Research), S.H.M.J. Houben (Magma Design Automation), E.J.W. ter Maten (Philips Research)
Tuesday, 16:30–17:00, Hall 11
To check for intended as well as unwanted (parasitic) oscillation in an electronic circuit, often transient simulation is employed. In transient simulation,
integration methods are used to solve the time-domain circuit equations. Unfortunately, the often-used BDF methods exert a rather strong damping on
the oscillatory solutions of the circuit equations. This may lead to the erroneous conclusion that no oscillation is present in a circuit that does actually
oscillate. To remedy this problem, modified integration methods have been
developed. Most of these are in the class of multi-step methods. The current contribution presents an alternative in the class of Runge-Kutta methods.
This alternative, a Diagonal Runge-Kutta (DRK) method, can be made to suit
oscillatory problems very well. A particular instance of a DRK method is
derived, which remains stable for large time-steps and has the property that
its damping can be tuned such that it becomes negligible for time steps in the
range of interest. These properties are verified numerically by application on
two oscillator problems.
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Reduced order models for eigenvalue problems
J. Rommes (Utrecht University)
Tuesday, 17:00–17:30, Hall 11
Two main approaches are known for the reduced order modeling of linear
time-invariant systems of state-space equations: Krylov subspace based and
SVD based approximation methods. The Krylov subspace methods try to
match the moments of the impulse response of the system. By making use of
existing (iterative) numerical schemes they have large-scale applicability. A
disadvantage is the absence of a global error bound. On the other hand, the
SVD based methods have global error bounds, in terms of the Hankel singular
values of the system. Moreover, they often preserve important properties
such as stability. However, these nice properties come at a price: the SVD
based methods consist of dense matrix computations and consequently there
is limited large-scale applicability.
In this talk features and short-comings of both types of methods will be
addressed. Furthermore, ideas for improvements will be discussed. It seems
attractive to take the best of both worlds and combine the Krylov subspace
based methods with the SVD based methods. Finally, the possible application of Jacobi-Davidson style methods such as JDQR and JDQZ for model
reduction will be explored. The Jacobi-Davidson method cannot be categorized as a Krylov based or SVD based method, but its specific convergence
properties may be of practical use in reduced order modeling. The possible
advantages and difficulties will be discussed. The application area consists of
problems originating from electric circuit simulation.
Preconditioners and flexible iterative solvers for the iterative solution of
linear systems in circuit simulation
U. Jaekel (NEC Europe Ltd), A. Basermann (NEC Europe Ltd), M. Nordhausen (Christian-Albrechts University)
Tuesday, 17:30–18:00, Hall 11
The performance of iterative Krylov subspace solvers for sparse linear systems in circuit simulation depends crucially on the quality of the preconditioners used. We compare combinations of flexible solvers with various preconditioners, and describe measures to improve the parallel efficiency of the
methods. Numerical experiments on transient simulation with NEC’s parallel
circuit simulator MUSASI are shown, comparing the performance of parallelized direct and iterative methods.
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Synthesis and Optimization of an On-Chip Power Grid
S.H.M.J. Houben (Magma Design Automation), R. Chou (Magma Design
Automation), L. Kruse (Magma Design Automation)
Tuesday, 18:00–18:30, Hall 11
Currently, on-chip power grids are designed by specialists who use their experience to come up with a power grid. Then, a validation tool such as Magma’s
Blast Rail is used to perform a voltage drop and current density analysis of
the resulting power grid.
Since this process of manual design and validation is time-consuming,
there is a strong tendency to over-design the power grid in order to avoid
too many iterations. However, over-designing the power mesh wastes chip
real estate. Preferably, this process of manual iteration should be replaced by
an automatic optimization step.
Much work has been done on the problem of optimally sizing a given circuit topology. The network graph is then taken as fixed, but the admittances
of the edges are to be changed by the optimizer. The cost function depends
on the admittances, and this function is minimized subject to the constraint
that voltages and voltage differences are within certain bounds.
Our approach generalizes this work in that we not only handle fixed topologies, but also allow certain classes of topology changes. In particular, the
number and spacing of wires in the power mesh can be computed by our
algorithm.
In our method, we split the optimization process into two steps. In the first
step, we model parts of the power mesh as continuous sheets of metal. We
find the required metal densities by solving an optimization problem. In the
second step, we approach the continuous sheet of metal by discrete wires,
taking into account various fabrication constraints on the width and spacing
of such wires.
Our method has been implemented in Magma’s low power synthesis tool
BlastPower. Numerical results are presented.
Minisymposium: Mathematics of (Portable) Energy Storage Devices
E.A. Verbitskiy (Philips Research Laboratories Eindhoven), P.H.L. Notten
(Philips Research)
Tuesday, 16:00–17:30, Hall 4
With a constant growth of added features and functionality to portable devices the problem of increased energy consumption, on one hand, and the
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demand for longer run times, on the other hand, are driving the development
of portable energy sources.
Rechargeable batteries are nowadays widely applied in the field of consumer electronics and (Hybrid) Electrical Vehicles (EV and HEV). Fuel Cells
are also gaining ground, with first products appearing on the market shortly.
Mathematical modelling, analyses and simulations of those devices offer
a great advantage over measurements. For example, less time is needed to
gain knowledge about the battery and fuel cell behaviour also in the interaction with other parts of a portable electronic device under a wide variety of
conditions.
The goal of this workshop is to present to a wide audience various aspects
of modelling of electrochemical systems, in general, and to demonstrate the
current work on modelling of Fuel Cells and rechargeable batteries, including
NiMH and Li-ion.
Mathematical Modelling and Optimization of Rechargeable Batteries
E.A. Verbitskiy (Philips Research Laboratories Eindhoven), P.H.L. Notten
(Philips Research Laboratories)
Tuesday, 16:00–16:30, Hall 4
Rechargeable batteries are nowadays widely applied in the field of consumer
electronics and (Hybrid) Electrical Vehicles (EV and HEV). Both NickelCadmium (NiCd), Nickel-Metal Hydride (NiMH) and Li-ion batteries are
used in these applications. Each battery type has its own specific advantages
and disadvantages. The design of efficient charging algorithms and accurate
state-of-charge indication methods are a continuous drive to come to optimal
battery management. In order to simulate the interaction between rechargeable batteries and the surrounding electronics, electrochemical models have
been set-up.
In this presentation we concentrate on the NiMH batteries. We discuss
various aspects of an electrochemical model which describes the developments of battery voltage, internal partial gas pressures and temperature. This
model contains a large number of paramaters, hence optimisation becomes a
difficult task. We present our approach to optimisation and demonstrate the
performance on real data.
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A Detailed Numerical Model for Direct Methanol Fuel Cells
J. Fuhrmann (WIAS), K. Gaertner (WIAS)
Tuesday, 16:30–17:00, Hall 4
In a joint effort between the Weierstrass Institute for Applied Analysis and
Stochastics (WIAS) and the Forschungszentrum Jülich, a detailed model for
Direct Methanol Fuel Cells has been developed.
The analytical description of this model is based upon systems of partial differential equations which describe catalytical reactions, chemical reactions, Stefan-Maxwell diffusion, multiphase flow in a porous medium with
mixed wettability, convective transport. The model has been implemented
in a research code developed by the WIAS. The code allows for both transient and stationary simulations, parameter variations and measurement fits
on one-, two- and three-dimensional unstructured meshes.
First, the talk will focus on the explanation of the model equations. After
discussing issues concerning discretization, numerical solution and implementation of the model, numerical examples will be shown. Comparisons to
measurements will be provided.
Mathematical models and their application in electrochemical reactor
design
J. Deconinck (Vrije Universiteit Brussel)
Tuesday, 17:00–17:30, Hall 4
The mathematical models governing transport of mass and charge in an electrochemical system are briefly explained. The electrolyte (convection, diffusion, migration and homogeneous reactions), the electrodes (migration) and
the interface (overpotentials) as well as thermal aspects will be considered.
From these general considerations simplified industrial models are derived
and it is shown how these models are integrated in a CAD environment and
are applied to design plating reactors and electroforming or electrochemical
machining processes. Next, the performances of more elaborated models are
presented:
- the high speed anodizing process where thermal effects are to be considered;
- simulations of chemistry and electrochemistry in cracks and crevices;
- simulations of pulsed electrodeposition of copper on a rotating disc electrode and a PCB through hole;
- the influence of turbulence models on the mass transfer at high Smidt numbers.
Finally some general considerations on future research directions are given:
- the interaction between measurements and models,
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- the need for more performing models (gas evolution, non-diluted solutions)
and improved measuring techniques,
- the link between local material properties (layer thickness, hardness, roughness, composition) and the local process quantities (concentrations, current
densities, temperature),
- the link between large scale continuum models and non-continuum molecular scale models.
Minisymposium: Mathematical modeling of glass 1
P. Kagan (Technische Universiteit Eindhoven)
Tuesday, 16:00–18:00, Hall 12
Over the last twenty years the mathematical modeling of various aspects of
glass production became a decisive factor in sustaining product competitiveness. The major objectives of the scientists are shape optimization, quality
improvement and energy consumption reduction. This minisymposium will
provide forum for mathematicians and engineers working on modeling of
fluid dynamics, heat transfer and chemical reaction aspects of glass related
processes. Dr. A. Wawrenczuk will present modern methodology and recent
results in modeling radiative heat transfer during cooling of melted glass. Dr.
F. Gonzales will demonstrate technology and results of modeling combustion process in glass feeder. Mrs. S. Allaart-Bruin and Dr. P. Kagan will
present modeling of blowing and pressing stages, respectively, of glass forming in production of bottles and tv screens. The proposed speakers have been
chosen from institutions leading the science and technology in the respective
fields.
FPM+radiation=mesh free approach in radiation problems
A. Wawrenczuk (Fraunhofer ITWM)
Tuesday, 16:00–16:30, Hall 12
Radiation problems arise in many industrially important cases. One of them
is glass cooling process, where radiation takes significant (for higher temperatures even major) part in heat exchange between material and its environment
and it also determines the rate of heat flow inside material. That is the reason
why any realistic approximation of the cooling must take into account this
effect.
Modern applications of glasses impose many hard to fill high-level demands on the properties of the final product, i.e. the glass itself. In order
to assure those properties the production process must be understood as well
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as possible and be thoroughly controlled. Temperature is currently the main
control parameter and it is strongly influenced by radiation. This leads to need
for effective and possibly fast modeling methods which would enable to predict the influence of external parameters (mainly temperature) on properties
of glass. This in turn requires the ability of efficient modeling of radiation.
In initial cooling phase glass is a viscous liquid with free, moving boundaries. Mesh free methods like SPH or FPM can be conveniently used in such
situations offering great flexibility and relative simplicity when compared to
mesh based methods. Therefore the idea of incorporating radiation into meshless method, like FPM, seems to be very attractive in respect to possible gains
it may bring.
This work is supposed to a give a short review of used radiation models (without more detailed look at them), next to discuss some vital aspects
of radiation heat transfer computations in mesh-free framework and, hopefully,present some numerical results for glass cooling.
Modeling of the Relevant Processes in the Feeder
F.J. Gonzalez Padilla (TPD-TNO)
Tuesday, 16:30–17:00, Hall 12
The increasing demands in quality, production efficiency and environmental
issues drives the glass producers towards optimization of their glass production process. Simulation models are very useful tool in understanding the
complex interaction between the glass melt and the combustion space, where
complex geometries and large amounts of small burners and coolers/openings
must be considered.
TNO has integrated in its glass tank model (GTM-X) the relevant phenomena in the feeder, among them height variation and combustion. The height of
the glass surface must be accurately predicted, since it influences the weight
of the glass gob used in the forming process. A glass level drawdown model
has been developed to predict the height of the glass level along the length
of the feeder as function of the pull rate, glass temperature, feeder slope and
geometry.
A simple but flexible combustion model has been developed. The model
allows for a realistic representation of the many burners present in the feeder.
Glass quality tools have also been implemented. These are important for
the numerical optimization of the glass production. This paper presents the
mathematical models used and discusses the results obtained.
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Modelling the press-blow process of container glass
S.M.A. Allaart-Bruin (Technische Universiteit Eindhoven)
Tuesday, 17:00–17:30, Hall 12
In cooperation with TNO Glass Group we are developing a simulation tool for
the final blowing step in container glass forming, which is characterised by
two free glass surfaces (in and outside) bounding a thin glass layer, radiative
cooling and reheating, moving contact lines and relatively fast conductive
cooling upon glass-to-mould contact. In this talk we focuss on the use of
the Level Set Methods for the free surfaces. We describe a re-initialization
procedure to preserve the level set function as a distance function, which is
needed to derive a accurate solution.
Modeling of glass pressing stage in bottle manufacturing
P. Kagan (Technische Universiteit Eindhoven), R.M.M. Mattheij (Technische Universiteit Eindhoven)
Tuesday, 17:30–18:00, Hall 12
Mathematical modeling of various aspects of glass behavior is a crucial constitutive of competitiveness of modern glass industry. Current work concentrates on modeling thermomechanical behavior of glass during pressing stage
of bottle manufacturing. Glass is modeled as an incompressible Newtonian
fluid with temperature dependent viscosity. Inertia and convective acceleration are neglected, and the flow is assumed to be dominated by viscous forces.
The problem is defined over an axisymmetric domain with curved nonconvex
boundaries. The computational domain varies continuously as the plunger
moves toward the mold. A free glass surface boundary is present and is modeled as a material surface. Glass deformation is regarded to be slow, so the
flow problem is solved at discrete time stages between which the computational domain is updated according to the free surface evolution kinematic
condition and kinematics of plunger motion. The flow problem is complicated by presence of thin thermal boundary layer in the glass near the mold.
Finite element method is exploited to cope with geometric and mechanical complexity of the problem. Straight edge triangle elements and second
degree approximation of velocity and temperature fields are used. Localized
behavior is captured with adaptively refined unstructured mesh. Local defect
correction approach is used to avoid ill conditioning due to large differences
in the size of finite elements involved in the same assembly. Stepwise mass
constancy, energy balance and refinement of space and time approximation
are used to validate the results. Ultimately, the presented results will be used
for optimizing the pressing stage of bottle manufacturing process.
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Minisymposium: How to train industrial mathematicians, II
J. Vladislavleva (Technische Universiteit Eindhoven)
Tuesday, 16:00–17:00, Hall 5
The post-graduate program Mathematics for Industry at the Technische Universiteit Eindhoven organizes a minisymposium titled: “How to train industrial mathematicians.”
The goal is to collect view points of people from science, industry, and training programs on the following subjects:
• What is the demand for ‘industrial mathematicians’ at the moment?
• How to select and educate students to become industrial mathematicians?
• What is the philosophy of programs with aforementioned objective?
• What is the appropriate ratio between gaining knowledge and gaining
skills?
Both the Mathematics for Industry program and the ECMI educational circuit
will benefit from this minisymposium since the questions addressing the vital
decisions that have to be made at every educational program will be posed
and discussed.
In this slot two speakers Mads Sørensen and Stef van Eijndhoven, both
possessing many years of experience in the education of industrial mathematicians, will show their approaches towards the training of industrial mathematicians. After that, we will organize a plenar discussion to come to a
fruitful exchange of opinions on this subject.
This part can be attended independently from the first part. For more information, contact:
Catherine Vladislavleva
Bertil van Zweeden
Cornè Botha
Tanya Barysenka
e-mail:
e-mail:
e-mail:
e-mail:
[email protected]
[email protected]
[email protected]
[email protected]
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Title to be announced
M.P. Sørensen (Technical University of Denmark)
Tuesday, 16:00–16:30, Hall 5
Industrial Mathematics Essentials
S.J.L. van Eijndhoven (Technische Universiteit Eindhoven)
Tuesday, 16:30–17:00, Hall 5
For long, mathematics was regarded as the mother of Science. Its necessity was without doubt and mathematicians did not see any need to prove the
essence of their existence. Being a pure academic science taking place at universities, mathematicians found their inspiration in the exact sciences. The
last century, considerable changes took place. Starting with the Industrial
Revolution, the engineering profession was introduced. Gradually, mathematics entered technology and mathematicians started to bother about the
role they could play in industry. The introduction of mathematics educational programs in the technological universities in the Netherlands marks the
beginning of an era where mathematics and technology are indissolubly connected. Not all mathematicians favored these developments and, still, not all
do. There seems a division into Pure Mathematics and Applied Mathematics, sometimes taking as synonyms for Good and Bad. Both take place in the
university environment with the only difference in the inspiration to carry out
research.
Industrial mathematics is Ugly. It is not inspired but it is driven by problems
from industry. Its result is not scientific papers; its result is solutions of problems in the form of algorithms combined with recommendations. The way to
come to a satisfactory results does not rely on mathematical quality, only; it
puts high demands on communication abilities and social skills. It requires
a type of personality mathematicians are not expected to posses in the wellknown caricatures. Relevance of Industrial Mathematics is without proof.
Existence of the Mathematics for Industry program within the Technische
Universiteit Eindhoven for more than 16 years with a total of 130 graduates,
is sufficient evidence. For this post-graduate program seeking for a balance
between mathematics-broadening and problem-solving components is a great
challenge. Selecting appropriate candidates and making participants responsible for their choices are unmistakably challenging as well.
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Minisymposium: Industrial and Financial Mathematics at
EURANDOM
A. Di Bucchianico (Technische Universiteit Eindhoven/EURANDOM), D.
Danilov (EURANDOM), T. Figarella (EURANDOM), M. Verschuere
(Vienna University of Technolog)
Tuesday, 16:00–17:30, Hall 7
Bergsma and Figarella discuss signature analysis for end-of-life management of electronic products. The ability to analyze and predict the (remaining) technical life of a product would make it possible either to re-use subassemblies, or to design products for which the technical and economical life
match. It is shown how wavelet analysis can be used to extract features from
electrical signals. ANOVA is used to establish relations between these features and performance degradation.
Danilov and Notten discuss a cycle life model for rechargeable Li-ion batteries. The model is capable to simulate both the charge-discharge behaviour
and long-term aging effects. The model consists of coupled differential equations that take into account several physical and electrochemical processes.
The model has been fitted to a wide range of experimental data and shows
good agreement.
Ladoucette discusses the large claims reinsurance treaty ECOMOR introduced by Thépaut, which has been largely neglected by most reinsurers because of its technical complexity. In this talk, she proposes new mathematical
results related to distributional problems of this reinsurance form which can
reopen the discussion on the usefulness of including the largest claims in the
decision making procedure.
Verschuere discusses a valuation model for European call options on power
spot prices due to de Jong and Huisman. The main goal of this talk is to
stress a shortcomings in their valuation procedure. These shortcomings come
assumptions like continuous-time variables and no-arbitrage theory, a choice
that can only be justified in case hedging strategies involving the underlying
commodity are admitted. An alternative solution is proposed. A closed valuation formula for simple spot price derivatives is derived based on actuarial,
rather than financial grounds.
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A multi-scale approach to functional signature analysis for product endof-life management
T. Figarella (EURANDOM), A. Di Bucchianico (EURANDOM), G. Hulsken
(Flextronics International), H.P. Wynn (Eurandom)
Tuesday, 16:00–16:30, Hall 7
Nowadays, electronic products tend to be economically outdated before their
technical end-of-life has been reached. The ability to analyze and predict the
(remaining) technical life of a product would make it possible either to reuse sub-assemblies in the manufacture process of new products, or to design
products for which the technical and economical life match. This requires
models to predict and monitor performance degradation profiles. In this paper
we report on designed experiments to obtain such models. We show how
wavelet analysis can be used to extract features from electrical signals. These
features are analyzed using the Analysis of Variance in order to establish
relations between these features and performance degradation.
Theory and Simulation of Lithium-ion Batteries: from single cycle performance to long-term aging effects.
D.L. Danilov (EURANDOM), P.H.L. Notten (Philips Research Laboratories)
Tuesday, 16:30–17:00, Hall 7
A mathematical model, describing the cycle life behavior of Li-ion batteries is
proposed. The model is a coupled system of ordinary and partial differential
equations and is capable of simulating both the charge-discharge behavior and
long-term aging effects. The following physical and electrochemical features
are taken into account.
• Main electrochemical storage reaction of intercalation of lithium in the
electrodes.
• Equilibrium potentials of intercalation electrodes.
• Butler-Volmer charge-transfer relationships at surfaces of electrodes.
• Diffusion of Li + ions inside the electrodes.
• Diffusion and migration of Li + and P F6− inside the electrolyte and the
Solid Electrolyte Interface (SEI).
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• Lithium consumption due to SEI formation on the negative electrode.
SEI formation is induced by electron tunnelling through SEI, leading to solvent reduction at the SEI/electrolyte interface. The fundamental quantum-mechanical relation for tunnelling current J has been
adopted.
• Degradation of the positive electrode as a result of the decomposition
of the active electrode material leading to inert electrode material with
respect to the main storage reaction. This results in capacity loss and
also in the deterioration of other electrode characteristics.
• Li-ion balance considerations are used. The total amount of lithium
inside the sealed battery is kept constant, while allocation of the lithium
ions changes.
The model has been fitted to a wide range of experimental data, including
charge and discharge voltage curves and capacity degradation curves during
cycling and shows good agreement. In particular, the model is capable to
explain the acceleration in capacity degradation of the Li-ion battery during
cycle life: the capacity can be limited either by the amount of the lithium ions
inside the battery or by the amount of active electrode material in the positive
electrode.
Reinsurance of Large Claims
S.A. Ladoucette (EURANDOM), S.A. Ladoucette (EURANDOM/Technical
University Eindhoven), J.L. Teugels (UCS, KUL)
Tuesday, 17:00–17:30, Hall 7
The large claims reinsurance treaty ECOMOR introduced by Thépaut (1950)
is well known not to be very popular and has been largely neglected by most
reinsurers because of its technical complexity. We propose new mathematical
results related to distributional problems of this reinsurance form which can
reopen the discussion on the usefulness of including the largest claims in the
decision making procedure. As such, we also examine more closely potential
applications of extreme value theory to reinsurance.
The ECOMOR treaty Rr (t) is defined via the upper order statistics of a
random sample. In some sense it rephrases the largest claims treaty, another
reinsurance treaty of extreme value type. It can also be considered as an
excess-of-loss treaty with a random retention determined by the (r + 1)th
largest claim related to a specific portfolio. Throughout, we assume the claim
number process {N (t), t ≥ 0} to be a counting process independent of the
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claim size process.
In a first part, we are interested in the asymptotic relation between the tail
of the distribution F of a claim size X and that of the quantity Rr (t). We
get accurate asymptotic equivalences and asymptotic bounds. Also, in the
sub-exponential case, we give a result showing the interplay between the accumulated claim amount and the reinsured quantity Rr (t).
In a second part, we turn to the ratio of the quantities Rr (t) and the accumulated claim amount. We give conditions that imply a dominant influence
of the quantities Rr (t) on this sum.
Finally, we touch on the question of convergence in distribution for some
quantities Rr (t). We get precise first and second order large deviation results
for the case where the claim size distribution F belongs to an extremal class,
eventually with remainder. The results are illustrated with some simulations.
Contributed presentations (theme: Financial mathematics/Geophysics)
Portfolio Analysis in Finance Mathematics
D.S. Hooda (Jaypee Institute of Engineering and Tech)
Tuesday, 16:00–16:20, Hall 14
In the present paper Markowitz’s method of mean-variance efficient frontier
has been explained. As there is a great association between risk and the uncertainty, so some measures of the risk based on entropy optimization principles
have been developed and studied. Risk aversion index and Pareto-optimal
sharing of risk have also been derived. In the end an application of maximum
entropy principle in risk sharing has been studied.
Fuzzy Binary Tree Model for European-Style Vanilla Options
H. Reynaerts (Ghent University), S. Muzzioli (University of Modena and
Reggi)
Tuesday, 16:20–16:40, Hall 14
The risk neutral valuation approach is widely used to price options and other
securities. In a binomial lattice setting (cf. Cox et al. (1979)) the derivation
of the risk neutral probabilities boils down to the solution of a linear system
of equations.
When the estimation of the system parameters is difficult, it may be convenient to let them take fuzzy values. Muzzioli and Toricelli (2001) are the
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first to adress the issue and to obtain a solution to the resulting system. Afterwards, Reynaerts and Vanmaele (2003) analyse a dual system of the latter
and obtain a different solution.
In a previous paper, Muzzioli and Reynaerts analyse dual fuzzy linear systems
of the most general form A1 x + b1 = A2 x + b2 , with A1 and A2 squared matrices of fuzzy coefficients and b1 and b2 fuzzy number vectors. They show
that the systems (A1 − A2 )x = b2 − b1 and A1 x + b1 = A2 x + b2 are equivalent in terms of vector solutions. They also propose a practical algorithm in
order to find the vector solution.
The aim of this paper is to reexamine the two solutions proposed in light of
the observations on dual fuzzy linear systems found in Muzzioli and Reynaerts (2004). The plan of the paper is the following. In the introduction we
recall the financial problem and we introduce the vector solution to dual fuzzy
linear systems. In Section 2 we highlight that the system, connected to the
financial problem, has no solution if one applies standard fuzzy arithmetic. In
Section 3 we propose the vector solution to that system and in Section 4 we
show the algorithm in order to compute the vector solution. The last section
concludes.
Comparison of Some Mixed Integer Non-linear Solution Approaches Applied to Process Plant Layout Problems
K.O.J. Westerlund (Åbo Akademi University), L.G. Papageorgiou (University College London)
Tuesday, 16:40–17:00, Hall 14
The Process Plant Layout (PPL) problem involves decisions concerning the
layout of a process plant consisting of a defined number of units and a limited
plant facility area. Spatial allocation of equipment items and the required connections between them are determined. Optimal plant layout is of great concern in both design of new industrial facilities and retrofit of existing plants
since it will affect the plant during its whole lifecycle.
PPL problems have mostly been solved by heuristic rules but in recent
years, significant research effort has been put on more rigorous methods
mainly based on mathematical programming techniques. The resulting problem has thereafter often been discretised in linear form and solved using linear solvers. In this paper, a non-linear approach to the general PPL problem
formulations is investigated. A comparative study between different nonlinear solvers is carried out and the performance of each solver is tested on
a set of problems. Both solution quality and computational efforts used are
critically evaluated. Four different solvers are evaluated, GAMS/DICOPT,
GAMS/SBB, α-ECP and GGPECP. The Outer Approximation method using
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an Augmented Penalty Function is used in DICOPT, the non-linear Branch
and Bound method in SBB, the generalised Extended Cutting Plane method
in α-ECP and a Generalised Geometric Programming approach integrated in
the Extended Cutting Plane method in GGPECP.
In the actual paper the solution results from the non-linear formulation is
compared to the results obtained by dicretising the non-linear model and solving the resulting model using a linear solver. Both solution quality and computational effort required for solution is critically evaluated. In the discretised
linear case the Mixed Integer Linear Programming (MILP) solver CPLEX
(version 8.0) is used.
Effective Estimation of Banking Liquidity Risk
P.C. Tobin (Swinburne University of Technology), A. Brown (Swinburne
University of Technology)
Tuesday, 17:00–17:20, Hall 14
Measurement of a bank’s exposure to liquidity risk both overall and on product line bases enables a bank to guard its financial security and bring accountability to individual management units. We examine a ‘bottom-up’ approach
on a specific banking case which provides simple and reliable estimates in all
but the most extreme cases. Critical problems identified include data availability - the task by the bank is to identify the worst 3 days in 10 000 - and
possible confounding with market risk.
Efficient Rank Reduction of Correlation Matrices
I Grubisic (Mathematical Institute Utrecht), R. Pietersz (ERIM, Erasmus
University)
Tuesday, 17:20–17:40, Hall 14
Geometric optimization algorithms are developed that efficiently find the
nearest low-rank correlation matrix. We show numerically that our methods outperform the existing methods in the literature. The algorithm is shown
to be globally convergent to a stationary point, with a quadratic local rate of
convergence. The connection with the Lagrange multiplier method is established, along with an identification of whether a local minimum is a global
minimum. The additional benefits of the geometric approach are: (i) any
weighted norm can be applied, and (ii) neighborhood search can straightforwardly be applied.
Coupling of open source geochemistry and transport tools for an efficient
geochemistry analysis
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A. Dimier (ANDRA), F.C. Francois Corrihons (Apside)
Tuesday, 17:40–18:00, Hall 14
The safety assessment of nuclear waste disposals needs to predict the migration of radionuclides and chemical species through porous media. In this context, ANDRA and CEA have launched the Alliances project to develop and
asses the necessary tools to analyze this phenomenology. In this scope, a tool
for geochemistry analysis has been set-up based on the geochemistry code
PhreeqC, and the two transport codes Mt3d and Traces, these three codes being open source. It has been validated on various configurations in and apart
of the nuclear context. It allows the evaluation of species evolution through
the medium, submitted, on the one hand, to transport phenomena including
convection, diffusion and dispersion; and on the other hand, to chemical reactions. Based on equilibrium chemistry, it enables aqueous solutions to interact
with minerals, exchangers and sorption surfaces. Kinetic reactions can also
be modeled. The coupling algorithm is sequential iterative, it uses a Picard
like method and enables various problem formulations. The tool uses python
as scripting language enabling an object oriented methodology. A user interface based on Qt for phenomenology definition, and Vtk for postprocessing
has been developed making the whole user friendly.
High Peclet Number Flows in a Slender 3D Lid Driven Cavity: Applications to Scraped Surface Heat Exchangers
M.E.M. Lee (University of Southampton), A.D. Fitt (University of Southampton), N. Hall Taylor (Chemtech International Ltd), C.P. Please (University of Southampton), (University of Reading), K.H. Sun (University of Warwick)
Tuesday, 16:00–16:20, Hall 13
Scraped-surface heat exchangers are widely used in the food industry to heat,
cool and sometimes to texture complex materials. In this paper heat transfer in a scraped-surface heat exchanger is considered for both Newtonian and
power-law fluids. The movement of the fluid is due to both axial pumping and
rotation of the scrapers. A chamber is enclosed by two neighbouring blades,
the inner rotating cylinder and the outer stationary cylinder. By taking a coordinate system moving with the blades this chamber is approximated by a
lid-driven cavity. The central idea is to exploit the high-Peclet number of
the flow in order to derive a two-dimensional averaged model, which significantly reduces computational effort. This model accounts for the long-term
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development of thermal boundary layers, both on the scraped-surfaces and the
stationary surfaces. Numerical results of the averaged model are presented
showing how both the average temperature and the variation in the temperature of the exit flow depend on the physical properties of the fluid, the geometry of the SSHE, the rotation rate and throughput. Results presented in this
paper are part of a multi-disciplinary research program supported by the EPSRC and the Faraday Partnership, and involves industralists from Chemtech
International and Tetrapak as well as academics.
Decision Support in Managing Fluids and Systems Applying Constraint
Logic Programming.
J.G.C.M. Goossens (WL | Delft Hydraulics), T. Creemers (UPC-CSICIRI), I. Pothof (WL | Delft Hydraulics), A. Heinsbroek (WL | Delft
Hydraulics)
Tuesday, 16:20–16:40, Hall 13
Modern Water Management is hardly possible without computer support
tools. Designing decisions, control schemes, operational strategies, etc. suffers from growing complexity due to many, often interactive, relevant aspects.
Decision Support Tools are generally built around a simulator that calculates
consequences of intended operations in a forward, cause >> effect direction.
The intended operations, however, must be invented by experts, without support by computer tools. In addition, the combinatorial nature of management
problems creates serious difficulties to invent good solutions, and improving solutions requires iterative, laborious cycles. To overcome some of these
drawbacks mathematical optimisation is applied. These techniques also suffer
from the combinatorics in the problem, so that problems have to be simplified
and long run times must be accepted. Decision Support can improve considerably by applying Constraint Logic Programming (CLP), a young programming paradigm successfully applied in Logistics, Planning and Scheduling,
and other Operations Research areas. This is shown by analysing the decision process and the way support is given by simulation based tools and by
CLP. CLP maintains a global view on the problem during solving and applies
a multidirectional reasoning over the problem aspects. Reasoning is done
as well from cause >> effect as from target >> required operations, guaranteeing that every generated solution meets the specified constraints. An
optimisation routine continuously generates improved solutions. The high
flexibility of the programming language allows for implementing complex
real world characteristics and requirements of the system, the problem and its
desired solutions (the constraints). These constraints are actively used to reduce the problem while solving it. Two applications in water management are
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shown, implemented in CLOCWiSe (Constraint Logic for Operational Control in Water Systems), a generic application builder for water management
problems. The implications for decision processes in water management are
discussed
A model for fluid flow in a scraped-surface heat exchanger
S.K. Wilson (University of Strathclyde, Glasgow), B.R. Duffy (University
of Strathclyde), M.E.M. Lee (University of Southampton)
Tuesday, 16:40–17:00, Hall 13
Scraped-surface heat exchangers (SSHEs) are used widely in the food industry to cook, sterilize and chill food. A SSHE comprises a cylindrical steel
annulus along which foodstuff is driven and a bank of blades rotating with
the inner cylinder that scrapes the foodstuff away from the heated or cooled
outer wall, preventing fouling and aiding mixing and heat transfer. Despite
their widespread application and much empirical engineering know-how, our
understanding of the fluid dynamics within a SSHE is still incomplete.
In this talk we present a simple mathematical model for fluid flow in a
SSHE in the case when the gaps between the blades and the walls of the device are narrow so that a lubrication-theory description is appropriate. Specifically we analyse steady isothermal flow of a Newtonian fluid around a periodic array of freely-pivoted scraper blades in a channel with one moving
and one stationary wall. Details of the flow structure are determined and, in
particular, the positions of the blades are calculated. We find that the desired
contact between the blades and the moving wall is attained if the blades are
pivoted sufficiently close to their ends. When the desired contact is achieved
the simple model predicts that the forces and torques on the blades are singular, and so the model is generalised to include three additional physical effects, specifically, non-Newtonian power-law behaviour, slip at rigid boundaries and cavitation in regions of low pressure, each of which is shown to
resolve these singularities.
This work forms part of a larger research project supported by the EPSRC
(Research Grant GR/R993032, Principal Investigator Prof. C.P. Please), and
by Chemtech International Ltd and Tetra Pak, under the auspices of the Faraday Partnership for Industrial Mathematics, managed by the Smith Institute.
New schemes for differential-algebraic stiff systems.
E. Alshina (Institute for Mathematical Modelling RAS), N.N. Kalitkin
(Institute for Mathematical Modelling RAS), A.B. Koryagina (MIET)
Tuesday, 17:00–17:20, Hall 13
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Many practical problems are described by systems of differential and algebraic equations. For example, while simulating non-stationary processes in
the electrical circuits algebraic Kirchhoff’s laws are taken into account, the
PDE system for gas dynamics is supplemented by algebraic condition equations. One or more differential equations in a system are possible implicit
u , t), where
algebraic. In general statement of the problem is M ddtuE = f (E
det M = 0 is a singular matrix. Additional difficulty for numerical solution
is following. All investigated problems are stiff. Stiff system is the problem
in which two or more physical processes have strongly distinguishing temporal characteristics. For example, while simulating processes in electrical
circuits the frequency of an alternating current is much greater than velocity
of amplitude modulation; in mathematical modeling of chemically reacting
gas flows tens chemical reactions with quite different speeds are taken into
account. Stiff systems are requiring the development of a special difference
scheme, with increased requirements to the stability. In this paper the sets 2stages difference schemes of Rosenbrock are tested. By results
of a theoreti
cal investigating two schemes L1-stable of accuracy O τ 2 and A - stable of
accuracy O τ 3 are recommended. Both autonomous and non-autonomous
problems are considered. Simulation of the transistor amplifier and gas flows
was carried out to illustrate possibility of the method. Numerical results confirm the effectiveness, high accuracy and suitability for stiff systems of these
schemes. This work is supported by RFBR (projects No’s 02-01-00066, 0301-00439), Russian Science Support Foundation, presidential programs of
support for scientific schools (project 1918.2003.1) and young Ph.D. (project
1907.2004.9).
Numerical solution of boundary value problems by a method of dynamic
potentials.
A.B. Alshin (Moscow State University)
Tuesday, 17:20–17:40, Hall 13
Some mathematical models of wave processes in ferromagnetics, semiconductors and in other media are reduced to initial boundary value problems for
Sobolev PDE . The investigation of such problems is traditionally carried out
by the method of dynamic potentials. The proof of existence of classical solution of initial boundary value problem is reduced to a proof of solvability for
some integral equation. In this work the dynamic potentials were constructed
for some new equations of Sobolev type and the existence and uniqueness
of classical solutions for main initial boundary value problems were proved.
The effective numerical was offered for this problem. This work is supported
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by RFBR (project No’s 02-01-00253), presidential programs of support for
scientific schools (project 1918.2003.1).
A CFL-like Constraint for Fast Marching Level Sets Method
F. Bernal (Universidad Carlos III de Madrid), R. Escobedo (Universidad
Carlos III de Madrid)
Tuesday, 17:40–18:00, Hall 13
Since the seminal paper of Osher and Sethian in 1988, level set methods
(LSM) are a widely used technique to solve problems in which the solution
has moving fronts. These methods, borrowed from hyperbolic conservation
laws, must fulfill a CFL condition. A particular case occurs when the velocity
of the front does not change sign. This is the so-called fast marching method
(FMM), for which no CFL condition is mentioned in the literature, to the best
of our knowledge.
We present numerical simulations which show that, depending on the velocity of the front, such a condition must be enforced in order to use Godunov’s scheme to solve the Eikonal equation. We present also an alternative
formulation of Godunov´s scheme that yields this constraint for the choice of
the space discretization, similar to a CFL condition. A physical interpretation
of this restriction is discussed.
On the effect of discontinuous properties of wood chips in the behaviour
of a digester
A. Araújo (University of Coimbra), J.A. Ferreira (University of Coimbra),
P. de Oliveira (University of Coimbra)
Tuesday, 18:00–18:20, Hall 13
The pulp and paper industry plays an important role in European economies.
The chemical reactions that transform wood chips in pulp occur mainly in a
complex moving bed reactor, the digester. Nowadays the use of mathematical models to simulate the transient behaviour of temperature and compound
concentrations represents a real need for industry because it allows simulation
of experiments that can not be afforded or that might be very risky. The digester - the most critical piece of the equipment - is an heterogeneous reactor
with an almost cylindrical shape, where wood chips react with an aqueous solution of sodium hydroxide and sodium sulfide, to remove the lignin from the
cellulose fibers. From a mathematical point of view the dynamical behaviour
of the reactor can be represented by a system of hyperbolic nonlinear partial
differential equations. In this system, with 15 equations, we can identify three
main types: the equations that describe the temperature and the concentration
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respectively of the solid, entrapped liquid and free liquid phase. Each one of
these type of equations present a certain complexity, its numerical simulation
being an hard task. In this sense we point out the high non linearity of the
functions that represents the chemical reactions; the discontinuities induced
by the extraction, enrichment and heat of the free liquor; the discontinuities
in the convection velocity of the free liquor - positive where the liquid flows
downwards and negative where the free liquid flows upwards . Numerical
methods based on operator splitting, nonuniform refinement and some particular techniques to smooth discontinuities, are studied from a qualitative and
quantitative viewpoint. Several simulations on temperature and concentrations of organics and inorganics compounds are presented. Special attention
will be devoted to the effects induced in the process by discontinuities of
wood chips composition.
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9:00–10:00
Plenary lecture
One for all: the potential approach to pricing and hedging (L.C.G. Rogers) 115
10:00–10:30
Break
10:30–12:30
Multiscaled Systems in Space and Time. (A. Bartel; theme: Electronic
industry) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Local error analysis of time integration methods for multiscaled coupled
problems. (A Kværnø) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Implementing efficient array traversing for FDTD-lumped element cosimulation (L.R. de Jussilainen Costa) . . . . . . . . . . . . . . . . . . . . . .
Hierarchical Models and Numerical Methods in Semiconductor Device
Transport Simulation: From Drift-Diffusion to Quantum Equations (S.R.
Sacco) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Numerical Simulation of Multirate Partial Differential-Algebraic Systems (S.
Knorr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation of multiphase flow and transport processes for industrial applications (F.A. Coutelieris; theme: Chemical technology) . . . . . . . . . .
Pore Network Modeling of Isothermal Drying in Porous Media (T. Stubos) .
On the Modeling of the Phase Separation of a Gelling Biopolymeric Mixture
(F.A. Coutelieris) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3D unsteady simulations of multiphase flow for industrial applications (O.
Simonin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Rainbow of Multi-Phase Flow Simulations (H. van den Akker) . . . . .
Mathematical modeling of glass II (P. Fusek; theme: Materials) . . . . . . .
Progress on the inverse problem for high precision glass forming (M. Sellier)
Compression of a hot glass cylindre (G.P. Kozyreff) . . . . . . . . . . . . .
Identification of nonlinear heat transfer laws (P. Fusek) . . . . . . . . . . . .
An Update of Fictive Temperature Theory (D. Gelder) . . . . . . . . . . . .
Wavelength averaged (gray) absorption coefficients for radiative transfer in
glass (N. Siedow) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Option valuation problems in financial mathematics (J.M. Schumacher;
theme: Financial mathematics) . . . . . . . . . . . . . . . . . . . . . . .
Valuation of collateralized debt obligations (P. Houweling) . . . . . . . . . .
Partially exact and bounded approximations for arithmetic Asian options (R.
Lord) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Measurement and valuation of interest rate risk within insurance contracts
(M.J.J. Janssen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Pricing high-dimensional American options using local consistency conditions (J.M. Schumacher) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiscale dynamics (J.G. Blom) . . . . . . . . . . . . . . . . . . . . . . . .
Aspects of multirate time integration methods in circuit simulation problems
(A. El Guennouni) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Coarse-grained simulation and bifurcation analysis using microscopic timesteppers (D. Roose) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hybrid Molecular Dynamics - Monte Carlo Simulations for Heat Transfer in
Micro and Nano-channels (A.J. Markvoort) . . . . . . . . . . . . . . . .
Case Studies from Study Groups with Industry (H. Ockendon) . . . . . . .
Problems and Solutions from the 47th ESGI in Denmark, August 2003. (P.G.
Hjorth) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modelling the growth of roses (V. Rottschäfer) . . . . . . . . . . . . . . . .
Modelling a densiometer (E. Cumberbatch) . . . . . . . . . . . . . . . . . .
Some cracking ideas on egg incubation (N.C. Ovenden) . . . . . . . . . . .
On the dynamics of a Bunsen flame (M.L. Bondar) . . . . . . . . . . . . . .
Solving the Maxwell equations for diffraction gratings with the C method
(N.P. van der Aa) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
High-order asymptotic approximation of three-dimensional fields within thin
thermo-elastic rods (O. Selsil) . . . . . . . . . . . . . . . . . . . . . . . .
The transfer of fibres in the carding machine (M.E.M. Lee) . . . . . . . . . .
Comparison of the Rigorous Coupled-Wave Analysis and Multiple Shooting
(M.G.M.M. van Kraaij) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stability Analysis of a Pipe Conveying Fluid with Multifrequency Pulsatile
Flow Velocity (L. Panda) . . . . . . . . . . . . . . . . . . . . . . . . . .
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One for all: the potential approach to pricing and hedging
L.C.G. Rogers (University of Cambridge)
Wednesday, 9:00–10:00, Blauwe Zaal
Various mathematical models of asset prices are widely used in the finance
industry; there is a bewildering blend of techniques, and very often different parts of the same financial house will use different models to analyse
essentially the same asset class. Harmonising the results for a firm-wide risk
analysis is then very difficult! In this talk, a general strategy is proposed for
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building a universal model which should be capable of handling all of the assets a firm deals with, and the ideas are illustrated with reference to interest
rate risk in many countries, and the associated exchange rates.
Minisymposium: Multiscaled Systems in Space and Time.
A. Bartel (Bergische Universität Wuppertal), R. Pulch (Bergische Universität
Wuppertal)
Wednesday, 10:30–12:30, Hall 11
This minisymposium addresses multiscaled problems which typically appear
in coupled, heterogeneous systems, or in complex integrated descriptions. We
like to discuss here the whole range from modeling to simulation, since these
problems may arise in the constraint industrial simulation (e.g., coupling of
simulators), where special setups have to be taken into account. And on the
other hand, there are efficient algorithms needed to enhance the simulation’s
performance as well as to enable the industrial simulation of larger, refined
systems.
We like to depict new ideas and directions to deal with these recent and
broad class of problems, cooperate with industry and to contribute to industrial tools and projects.
Local error analysis of time integration methods for multiscaled coupled
problems.
A Kværnø (NTNU)
In many applications we have to deal with time integration of coupled systems, in particular with subsystems of different time scales. Over the years,
several approaches have been developed to exploit the particular properties of
each subsystem, like multirate methods, implicit-explicit methods and splitting methods. More recently, also exponential integrators are enjoying a renaissance. Most of these methods are well understood in terms of classical
local error / order analysis. However, the desired modus operandi often gives
stepsizes larger than the time scales of the rapid subsystems. In this case, the
classical order analysis is of limited, although important, relevance.
In this talk, we will focus on the error behaviour of the above mentioned
methods for coupled systems when comparable large stepsizes are used.
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Implementing efficient array traversing for FDTD-lumped element cosimulation
L.R. de Jussilainen Costa (Helsinki University of Technology)
Multiscale systems in time and space, such as cosimulation with an FDTDbased electromagnetic (EM) simulator and a circuit simulator, requires several large arrays to contain data. The choice of data type implementing these
arrays significantly affects the execution speed of the resulting executable
program. The results of this study indicate that this choice is dependent on
the compiler used to compile the executable and possibly on the platform
used to run it. Another important aspect is traversing these arrays to access
or update data using nested loops. How this is done also affects the execution speed. Two data types were used to implement the arrays in the C
programming language. These arrays were traversed in a manner natural to
the language and in another more efficient manner. The traversing to access
and update the data emulated the FDTD method since this is the computationally more demanding analysis in the EM–lumped element cosimulation.
Simulations on four computer platforms showed significant speed-up when
the efficient traversing routine was used to traverse both data types. This indicates that the routines used by compilers to optimise the executable code
have not yet developed to the point where they always find the fastest possible machine code. This provides the means to squeeze better performance
from the executable without changing the mathematics involved. The arrays
and traversing techniques can be implemented as C macros, creating a macro
language to implement the nested loops and the traversing for data accessing
and updating. This macro language ensures that the code is readable and understandable. Although this study used the C language, similar results may
be expected in other programming languages as well.
Hierarchical Models and Numerical Methods in Semiconductor Device
Transport Simulation: From Drift-Diffusion to Quantum Equations
S.R. Sacco (Politecnico di Milano)
In this lecture, a critical overview of mathematical transport models for semiconductor device simulation is addressed. An hierarchy of models is considered, ranging from classical Drift-Diffusion equations, up to touch Quantum
Models for nanoscale-sized devices. For each specific model in the hierarchy,
an analysis of its limit of validity is carried out, and appropriate functional
and numerical techniques are discussed for discretization. Several examples
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illustrate the performance of models and methods in the simulation of real-life
devices.
Numerical Simulation of Multirate Partial Differential-Algebraic Systems
S. Knorr (University of Wuppertal), R. Pulch (University of Wuppertal)
In radio frequency (RF) circuit design, signals with widely separated time
scales arise. The numerical simulation of such signals causes a large amount
of computational work in a standard transient analysis, because the slowest
time scale determines the integration intervall, whereas the fastest time scale
restricts the integration step size. In contrast, a multidimensional model yields
an alternative approach, where for each time scale a corresponding variable is
introduced. This transition transfers the differential-algebraic system (DAE)
of the network equations to a multirate system of partial differential-algebraic
equations (MPDAE). Here the different time scales are decoupled and the
arising MPDAE can be solved efficiently.
In this talk a specially tailored method of characteristics is described, which
enables an efficient simulation of the MPDAE. Furthermore, to address stability properties, some index considerations are discussed.
Minisymposium: Simulation of multiphase flow and transport processes
for industrial applications
F.A. Coutelieris (Unilever), J. Janssen (Unilever)
Multiphase flow processes are of significant interest in many industrial applications such as food, textile, ceramics, granular media and pharmaceuticals
while they are also involved in distillation and vaporization processes associated with soil remediation as well as in the recovery of volatile oil components from reservoirs by gas injection. A wide range of mathematical tools
have been developed for the numerical simulation of multiphase flow and
transport processes within a variety of geometries. In this minisymposium
we will present various simulations techniques for the 2- and 3-phase flow
problems (artificial compressibility algorithm, PISO, etc.). Relative simulations for mass transport by advection/convection and diffusion will also be
presented taking into account chemical reactions in some cases. Since that the
coverage of the broadest potential range of aspects for applications of multiphase flow is among the scopes of this minisymposium, we willl present:
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1. The modeling of isothermal drying in porous media and the mass transfer by advection and diffusion by using a 2-D pore network model.
2. The modeling of phase separation and gelation of a biopolymer mixture
under simple shear flow and a constant temperature gradient by using the Sγ
method.
3. The modeling of bubbly flow in various geometries taking into account
hydrodynamical phenomena like break up and coalescence of bubbles
4. The modeling of particles flow under various flows regimes (including
turbulence) as well as their interactions (collision models).
The mathematical interest for the simulation of multiphase flow and transport could be considered high, since four high level laboratories (both for
universities and the industry) have put significant effort on that. On the other
hand, industry is obviously strongly interested in their results since the organizer of the proposed minisymposium is one of the biggest food industries
worldwide.
Pore Network Modeling of Isothermal Drying in Porous Media
T. Stubos (NCSR DEMOKRITOS), A.G. Yiotis (NCSR DEMOKRITOS),
A.G. Boudovis (NTUA), Y.C. Yortsos (University Southern California)
Drying of porous materials is a two-phase flow process of significant interest
in many industrial applications such as coatings, food, paper, textile, wood,
ceramics, building materials, granular media, electronic devices and pharmaceuticals. In a different context, the process of drying in porous media is
also involved in distillation and vaporization processes associated with soil
remediation as well as in the recovery of volatile oil components from reservoirs by gas injection. In general, a single- or multi-component liquid phase
gradually evaporates during drying and is removed from the porous structure
via combined heat and mass transfer. Traditional descriptions of the process
rely on phenomenological approaches, in which the porous medium is a continuum, the dependent variables, like moisture content, are volume-averaged
quantities and the relation of fluxes to gradients is through empirical coefficients. Such approaches essentially ignore the effect of the pore microstructure which is of key importance for a quantitative understanding of the process. In this paper we present numerical results obtained from a pore network
model for the drying of porous media that accounts for various processes at
the pore-scale. These include mass transfer by advection and diffusion in the
gas phase, viscous flow in liquid and gas phases and capillary effects at the
gas-liquid menisci in the pore throats. We extend our work by studying the
effect of capillarity-driven viscous flow through macroscopic liquid films at
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the pore level. A mathematical model that accounts for viscous flow in a
2-D pore network both through the liquid films and the bulk liquid phase is
presented. It is shown that film flow is a major transport mechanism in the
drying of porous materials, its effect being dominant when capillarity controls
the process, which is the case in typical applications.
On the Modeling of the Phase Separation of a Gelling Biopolymeric Mixture
F.A. Coutelieris (Unilever), V.A.A.G. Haagh (Unilever), W.G.M. Agterof
(Unilever)
The gelation of polymer mixtures under constant cooling rate has been found
to be an attractive product structuring mechanism for the food industry. As
applications become wider, a predictive method for the process is warranted.
To this end, we apply the so-called ”Sγ concept” in a CFD module for the
modeling for microstructure formation of gelling mixtures, where moments
of the particle size distribution are evaluated using the local flow conditions
as obtained from CFD simulations for the processes considered. The major driving force for these processes is the competition between phase separation, gelation and hydrodynamic phenomena such as break-up and coalescence. Based on theoretical investigations, analytical expressions for the
source terms representing the hydrodynamics (break up and coalescence of
the droplets) as well as the gelation process were produced. Constitutive
models are developed to incorporate the effects of phase separation and gelation on the rheology of the phases. The numerical procedure was successfully
validated against experimental results for various polymeric mixtures, rheological conditions and temperatures. Finally, the simulations for different
cooling rates clarified the inter-relationships between the competitive mechanisms by depicting the time interval of the domination of each.
3D unsteady simulations of multiphase flow for industrial applications
O. Simonin (IMFT)
A 3-D transient gas-liquid-solid three-phase flow model is under development and validation to investigate the local hydrodynamic of industrial applications such as feed injection region of FCC riser reactors, combustion in
CFB boilers or mixing in polymerisation reactors. The model is based on the
Eulerian multifluid approach in which separate transport equations of mass,
momentum and enthalpy are computed for the gaseous, feed-spray droplet
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and particle phases. The turbulence of the gaseous mixture is predicted using a k − ε model accounting for the modulation by the dispersed phases.
The microscale fluctuating motions and transport properties of the particle
and droplet phases are modelled using separate two-equation modelling approaches, predicting the particle kinetic energy and fluid-particle covariance,
developed in the frame of kinetic theory of granular medium but accounting
simultaneously for particle-particle and fluid-particle interactions. A simplified catalytic reaction kinetic is also incorporated in few simulations mainly
to account for the endothermic heat and for the expansion of the gaseous
mixture. Theoretical validation of the closure model assumptions is carried
out by performing Discrete Particle Simulation of colliding particles coupled
with the fluid flow computation. The simulations are performed using a CFD
solver based on a finite volume spatial discretisation with collocated arrangement of all variables developed by Electricité de France.
The Rainbow of Multi-Phase Flow Simulations
H. van den Akker (TU Delft)
This review is about selecting the best approach for simulating multi-phase
flows for industrial applications. Each time, the quest is for a balanced choice
between the need of the simplest answer to the industrial problem definition
and the temptation of simulating the underlying physics and chemistry given
the ever increasing potential of computers and CFD software.
The pros and cons of Reynolds-Averaged Navier-Stokes (RANS) Simulations, Large-Eddy Simulations (LES) and Direct Numerical Simulations
(DNS) are evaluated. The relevance of proper numerical solvers is discussed.
Three series of simulations of varying sophistication illustrate the potential
and the difficulties of a hierarchical approach.
Minisymposium: Mathematical modeling of glass II
P. Fusek (Johannes Kepler University Linz)
Participants:
• Mathieu Sellier, Horst Loch, Schott Glas, Mainz, Germany
Norbert Siedow, ITWM, Kaiserslautern, Germany
• Laurent Duchemin, Cambridge University, UK
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• Gregory Kozyreff, Oxford University, UK
• Peter Fusek, Johannes Kepler University Linz, Austria
• David Gelder, Independent Consultant, UK
The significance of mathematical modeling for the glass industry has been
steadily increasing. This minisymposium deals therefore with some of the
major questions that arise in this field: shape optimization, levitation, heat
transfer and fictive temperature. Mathieu Sellier will address the inverse problem that occurs in the process of high precision glass pressing, i.e. the question of choosing the optimal design of the mould and the right temperature
regime during glass forming in order to obtain a prescribed glass geometry.
As it turns out, the design space is very large and an optimization procedure
is necessary. Laurent Duchemin and Gregory Kozyreff will present two models describing the levitation of a drop of molten glass above a porous mould
through which air is injected. Peter Fusek will describe the nonlinear inverse
problem of identifying the heat transfer coefficient between the glass and the
mould corresponding to the observed temperatures. In this context another
approach will be suggested, where the operator under consideration becomes
linear. In the talk by David Gelder the issue of fictive temperature will be dicussed. Even though fictive temeperature forms a very convenient structural
parameter, it does not correctly represent glass properties for temperatures far
away from the annealing temperature. For this reason an alternative structural
parameter to the fictive temperature will be suggested and described.
Progress on the inverse problem for high precision glass forming
M. Sellier (Schott Glas/ITWM), H. Loch (Schott Glas), N. Siedow (ITWM)
The question of interest in the present work is the inverse problem for high
precision glass pressing, i.e. ‘How to design the mould and the temperature
regime so that at the very end of the forming process we will get at room temperature a prescribed glass geometry with a precision in the order of the Micron?’. The aim is to reduce and possibly eliminate completely from the manufacturing process the necessary post-processing stage when the final shape
does not conform to the desired one.
Relying on experimental trial and error to address this problem is extremely
costly, time consuming and success is not guaranteed. Of course, the use
of computer-aided simulation to solve the direct problem allows significant
progress in the search of the optimal design. However, in the present case,
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the design space consisting in the initial mould shape and the temperature
history is very large and an optimization procedure is necessary. Moreover,
the rheological behaviour of the glass is very complex involving stress and
structural relaxation. These can be accounted for using Narayanaswamy’s
model and introducing the concept of fictive temperature.
Preliminary numerical results concerning the sensitivity analysis of an axisymmetric, freely cooled, glass piece to its initial shape and temperature
regime will be presented.
Compression of a hot glass cylindre
G.P. Kozyreff (Math. Institute, Oxford University)
Simple compression experiments in high temperature ovens are sometimes
used to measure the visco-elastic coefficients of liquid glass. It has recently
been reported that, under some circumstances, the deformed cylindre acquires
an unexpected ‘inverse-barrel’ shape. This has been correlated to the formation of a thin crystalline skin on the outside of the cylindre. In this presentation, we show how a simple buckling model for that skin explains the
observation.
Identification of nonlinear heat transfer laws
P. Fusek (Johannes Kepler University Linz)
The correct description of the heat transfer between glass and the surroundings is a very important issue for glass production. Especially in hot forming, the product quality depends on the heat transfer between glass and the
mold. Our task is to determine the heat transfer coefficient corresponding to
the observed temperature which turns out to be an ill-posed inverse problem
(small errors in the observations can produce large variations of the corresponding coefficients). In order to overcome the ill-posedness, one can apply
the Tikhonov regularization to the forward operator. In this context, another
approach will be suggested where the operator under consideration becomes
linear. Such procedures can be of great benefit especially in cases when the
classical forward operator does not possess sufficiently good properties.
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An Update of Fictive Temperature Theory
D. Gelder (Consultant-Mathematics for Manufacturers)
Properties of glasses of given composition do not depend solely on temperature. However for normal glass-making and product requirements, and often to the accuracy of measurement, many properties are linearly related.
They can therefore be defined by temperature and a ‘structural parameter’.
Around and below the annealing temperature glass is not necessarily in structural equilibrium. However for annealed products the structure is found to
be in equilibrium somewhere around the annealing temperature. Cold density - and therefore other properties - are linearly related to this equilibrium
temperature. It is conventionally defined as the ‘Fictive Temperature’ and
forms a convenient structural parameter. For many decades it has given good
understanding of structural changes during processing.
However the concept does not correctly represent glass properties outside
perhaps 50◦ C below to 150◦ C above the annealing temperature. Various problems with using it outside this range are described. In isolation they can be
resolved by various speculations about structural changes, but the nature of
these has not permitted direct experimental verification. No simple approach
covering even a substantial proportion of the anomalies has been established.
Recent work of Kieffer shows that above the annealing temperature viscoelastic properties can indicate a two-phase structure. A better connected structure
predominates at lower temperatures, a more loosely connected structure at
higher temperatures. The fraction f of higher temperature structure is linked
to temperature by a simple formula. Here use of f as an alternative parameter
to fictive temperature is explored, in particular for density. The success of the
fictive temperature concept is ‘explained’ by a point of inflection in the graph
of f against temperature, giving a nearly linear range.
Wavelength averaged (gray) absorption coefficients for radiative transfer
in glass
N. Siedow (Fraunhofer ITWM), R. Wegener (Fraunhofer ITWM)
The production of glass and glassware is a very complex process influenced
by many technical and physical parameters. One of the most important parameters of making high quality glasses is the temperature. Almost all production steps are influenced by the temperature distribution within the glass.
First, during the melting process, the temperature distribution in the glass
tanks affects the convection behaviour and thus the homogeneity of the glass.
The flow behaviour of glass during high temperature forming is controlled
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by the temperature distribution. Finally, the time-space temperature distribution is responsible for the strains frozen within the glass during the cooling
process. Glass is a semitransparent material. The heat transfer is accomplished not only by conduction but also by radiation. Especially for high
temperatures radiation is the dominant process of heat transfer and can not
be neglected. Inside the glass infrared radiation is absorbed and emitted with
respect to the Planck’s law. The coupling between heat and radiative transfer
equation is non-linear and high-dimensional. In general the absorption coefficient is temperature and wavelength dependent. For numerical simulation
of radiative heat transfer problems the absorption coefficient is divided into
piecewise constant values (bands) with respect to the wavelength. For practical relevant simulations one has to take into account about 10 to 20 different
bands. Thus, the minimization of the number of wavelength bands is important for the efficiency of numerical simulation of real-world problems. In the
present paper the derivation, advantages and limitations of mean absorption
coefficients known from literature, like Planck- or Rosseland-mean absorption coefficient, are discussed. A new Planck-Rosseland-superposition mean
absorption coefficient will be presented and used to simulate the cooling of
hot glasses.
Minisymposium: Option valuation problems in financial mathematics
J.M. Schumacher (Tilburg University), P.J.J. Ferket (Robeco), R. Lord
(Rabobank International)
The purpose of the minisymposium is to demonstrate various aspects of option pricing problems as they arise in the daily practice of financial institutions. The following presentations are planned:
• Valuation of collateralized debt obligations
Patrick Houweling (Quantitative Research, Robeco Asset Management)
• Partially exact and bounded approximations for arithmetic Asian options
Roger Lord (Tinbergen Institute, Erasmus University Rotterdam and
Modelling and Research, Rabobank International)
• Measurement and valuation of interest rate risk within insurance contracts
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Michiel Janssen (Concern Finance & Control, Group Actuarial Department, Interpolis)
• Pricing high-dimensional American options using local consistency
conditions
Steffan Berridge (Dept. of Econometrics & OR, Tilburg University) and
Hans Schumacher (Dept. of Econometrics & OR, Tilburg University).
The first paper considers an option pricing problem in the context of interest
rate instruments where the standard Black-Scholes model cannot be used; the
paper therefore focuses on modeling problems, in particular the modeling of
correlations. The second paper does stay within the framework of the standard Black-Scholes model, but considers a nonstandard type of option which
has to be valued by means of numerical methods; the challenge here is to
make use of the particular option structure in order to arrive at a fast computational scheme. In the third paper, the valuation of optional features in
insurance contracts is discussed, which is a subject of considerable practical
interest. Finally, the fourth paper emphasizes computational aspects again.
The standard Black-Scholes model which essentially has only one state variable is replaced by a model with more (3 to 10) state variables, and the challenge is addressed of numerically solving a free-boundary partial differential
equation in this number of variables.
Valuation of collateralized debt obligations
P. Houweling (Robeco Asset Management)
This presentation deals with the valuation of collateralized debt obligations
(CDOs). A CDO is a structure of fixed-income securities, called the tranches,
whose cash flows are backed by the payments of an underlying pool of debt
instruments, the collateral, through a set of rules, the waterfall structure. Income from the collateral is first paid to the senior tranches, than to the mezzanine tranches and finally to the equity tranches. A CDO allows the redistribution of the risk of the collateral to create securities with a variety of risk
profiles. The primary risk is the occurrence of defaults. The key input to
the valuation of a CDO is therefore the joint default time distribution of the
issuers of the collateral instruments. The first part of the presentation covers the specification and estimation of the default time model. We separately
model the marginal distributions and the dependency structure, for which we
use a copula function. The model has a so-called structural interpretation:
an issuer defaults if its asset value drops below a threshold value, which is
derived from the marginal distribution; the copula function can be interpreted
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as the dependency of the asset returns. We estimate the model as follows: for
the marginal distributions, we calibrate the empirical distribution function on
market quotes of credit default swaps (CDS); the dependency structure is estimated on time series of asset returns. In the second part of the presentation,
we apply the default time model to the riskneutral valuation of a CDO. Due
to the complexity of the waterfall structure, an analytic solution is not available. Therefore, we resort to Monte Carlo simulation. To reduce the required
number of simulations, we apply several variance reduction techniques. In
addition to the value of the CDO, we also look at sensitivities to several input
parameters.
Partially exact and bounded approximations for arithmetic Asian options
R. Lord (Tinbergen Institute, Erasmus University Rotterdam)
This paper considers the pricing of European Asian options in the BlackScholes framework. Firstly we consider the partial differential equation approach to the pricing of Asian options. We show the link between the approaches of Rogers and Shi [1995], Andreasen [1999] and Večeř [2001]. For
the latter formulation we propose two reductions, which increase the numerical stability and reduce the calculation time. Secondly, we show how a closedform expression can be derived for Rogers and Shi’s lower bound for the general case of multiple underlyings. Thirdly, we sharpen Thompson’s [1999]
upper bound for the value of an Asian option. This is important for the practically relevant case of options with long maturities. Numerical results show
that when the strike price is not extremely high, the resulting upper bound
is tighter than recently introduced upper bounds in studies by Nielsen and
Sandmann [2003] and Vanmaele et al. [2002]. Finally, we consider analytical approximations for the value of an Asian option. A much heard criticism on moment-matching approaches is that the error in the approximation
is not known beforehand. We combine the traditional moment-matching approaches (e.g. Levy [1992]) with the conditioning approaches (e.g. Curran
[1994]) and introduce a new class of analytical approximations, which can be
proven to lie between a sharp lower and upper bound. In numerical examples
the accuracy of these new approximations is demonstrated. The approximations are found to outperform all of the current state-of-the-art upper bounds
and approximations.
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Measurement and valuation of interest rate risk within insurance contracts
M.J.J. Janssen (Interpolis NV)
Many insurance contracts contain embedded options. In the past insurance
companies valued their contracts without taking into account the current term
structure of interest rates or the value of these embedded options. With the
fair value calculations of insurance contracts currently at the centre of attention, quantifying the risk attached to these embedded options is of the utmost
importance. Not only is it expected that in a number of years regulators will
enforce fair value calculation for insurance contracts, there are also sounds
reasons from the world of arbitrage pricing to favour the fair value approach.
If this approach is to be implemented, fluctuations in market rates will have
a direct impact on the balance sheet of the insurance company. Not only will
an insurance company take a different view on her investment policy, it will
also be important to measure and hedge the interest rate risk on her liabilities.
In the first part of the presentation we will show how a one-factor Hull and
White model can be used for the valuation of insurance contracts including
embedded options. We will focus on insurance contracts including profit sharing. Hereafter we will show how to use a first order Vector Autoregressive
Model in combination with a Nelson-Siegel model to describe the behaviour
of interest rates through time. This model will be used to illustrate the consequences - in terms of risk profile and investment strategy - of implementing a
fair value approach for an insurance company.
Pricing high-dimensional American options using local consistency conditions
J.M. Schumacher (Tilburg University), S.J. Berridge (Tilburg University)
We investigate a new method for pricing high-dimensional American options.
The method is of finite difference type but is also related to Monte Carlo techniques in that it involves a representative sampling of the underlying variables. An approximating Markov chain is built using this sampling and linear
programming is used to satisfy local consistency conditions at each point related to the infinitesimal generator or transition density. The algorithm for
constructing the matrix can be parallelised easily; moreover once it has been
obtained it can be reused to generate quick solutions for a large class of related problems. We provide pricing results for geometric average options in
up to ten dimensions, and compare these with accurate benchmarks.
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Minisymposium: Multiscale dynamics
J.G. Blom (CWI, Amsterdam), J.F. Williams (CWI)
Many important physical problems under consideration today exhibit behaviour on vastly different time or space scales. A common research goal
is to understand how to resolve the effects of fast time-scale behaviour over
long times without complete resolution of that fast behaviour. In this minisymposium we would like to bring together researchers from different areas
of numerical analysis and applications addressing this problem.
Aspects of multirate time integration methods in circuit simulation problems
A. El Guennouni (Philips Research and Yacht Technology)
We present a new robust compound strategy for multirate time integration
methods. The strategy applies to DAEs and to time-dependent PDEs as well.
We will compare this to other known strategies like Slowest First and Fastest
First. The new strategy elegantly fits hierarchical circuit definition. Furthermore, the impact of the partitioning will be considered. Finally, because in
circuit simulation discontinuities often occur, special attention will be paid a
careful treatment of these discontinuity problems. The effectiveness of the
method will be illustrated by numerical results.
Coarse-grained simulation and bifurcation analysis using microscopic
time-steppers
D. Roose (K.U. Leuven), G. Samaey (K.U.Leuven), P. van Leemput
(K.U.Leuven)
An important class of problems exhibits smooth behaviour in macroscopic
space and time, while only a microscopic evolution law is known. For such
time-dependent multi-scale problems, a so-called ‘equation-free’ framework
has been proposed by Kevrekidis and collaborators. It is assumed that one
has information about the variables that determine evolution on macroscopic
time and length scales, but one is unable to obtain a closed model (differential
equations). The key idea is to extract information on the evolution of these
macroscopic variables through appropriately initialized simulations using the
(given) microscopic evolution law on small domains for short time intervals.
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This information is subsequently used to construct a ’coarse-grained’ timestepper for the macroscopic variables. Once an accurate coarse-grained timestepper is constructed, one can perform more general tasks, such as the computation and stability analysis of steady states and limit cycles, using software
for time-stepper based numerical bifurcation analysis with the coarse-grained
time-stepper.
In this talk, we will focus on two aspects of this approach, namely the
gap-tooth scheme for homogenization problems and coarse-grained numerical bifurcation analysis of lattice Boltzmann models. In both studies, the
numerical accuracy is examined closely.
When the microscopic problem is a reaction-diffusion homogenization
problem, we show how the gap-tooth scheme approximates a finite difference scheme for the homogenized (constant coefficient) equation, using only
the microscopic problem in a number of small boxes (which correspond to
macroscopic mesh points). We examine how the box width and box boundary conditions affect the obtained accuracy.
We also show how to perform coarse-grained bifurcation analysis using as
an illustrative example a lattice Boltzmann model equivalent to the FitzHughNagumo partial differential equations. We study how the initialization of the
microscopic simulations affects overall accuracy and efficiency.
Hybrid Molecular Dynamics - Monte Carlo Simulations for Heat Transfer in Micro and Nano-channels
A.J. Markvoort (Technische Universiteit Eindhoven), P.A.J. Hilbers (Technische Universiteit Eindhoven), S.V. Nedea (Technische Universiteit
Eindhoven), A.A. van Steenhoven (Technische Universiteit Eindhoven)
For optimal performance and lifetime of electrical components, it is essential
to cool these components, since they produce heat when operating. Because
most electrical components become smaller and smaller and the power consumption continuously increases, the standard cooling techniques start to fail.
Therefore, more efficient cooling techniques, like microchannel cooling with
phase transition, are necessary.
In order to study the effect of the channel size on the heat flow through such
a channel, detailed knowledge of the flow profile is needed. However, when
the channel size decreases, the continuum approach to model such channels
is no longer applicable. At Knudsen numbers larger than approximately 0.1,
particle based methods should be used instead. Several such methods exist.
A standard method for studying particle dynamics is Molecular Dynamics.
From a physical point of view, this is a suitable method, but this method is
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computationally too expensive to use for microchannels. To handle larger
time frames, a Monte Carlo method can be employed, but this is at the expense of less accuracy near the channel walls.
We have combined Molecular Dynamics with a Monte Carlo method such
that we can use the advantages of both methods: molecular dynamics near the
boundaries, because of the accuracy, and Monte Carlo in the bulk, because of
the lower computational costs.
The feasability of the scheme is demonstated by modelling a dense gas in
a channel where both walls have a different temperature.
Minisymposium: Case Studies from Study Groups with Industry
H. Ockendon (Oxford University)
The Study Groups with Industry were started in Oxford in 1968 and since
then the idea has spread around the world. In particular there are now 4
study group meetings in Europe every year. In this minisymposium we will
describe a number of problems which were brought by industry to a recent
Study Group meeting and what the outcome was. Examples from meetings
in Denmark, Holland and the UK will be described.
Problems and Solutions from the 47th ESGI in Denmark, August 2003.
P.G. Hjorth (University of Southern Denmark)
The problems posed by industry for the 47th European Study Group held in
August 2003 ranged from trivial to extremly hard. I will very briefly review
the five problems and also their (re)solution by the international joint strike
force of mathematicians assembled in the Danish countryside in the late summer 2003.
Modelling the growth of roses
V. Rottschäfer (Universiteit Leiden), H. Ockendon (Oxford University)
At the 42nd ESGI in Amsterdam the question of how rose productin in greenhouse can be optimised was considered. A rose growth model was derived
that can be used to predict the rose harvest . The model is made up of the
following parts: (i) a local model that calculates the photosynthetic rate per
area of leaf and (ii) a global model of the greenhouse that transforms the
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photosynthesis of the leaves into an increase in mass of the rose crop. In
the local model it was found that the photosynthesis depends not only on the
timedependent ambient conditions which include temperature,humidity, carbon dioxide concentration and light intensity but also on the location and age
distribution of of the leaves and the form of the underlying rosebush. This
was one of the major difficulties that had to be resolved before formulating
the global model.
Modelling a densiometer
E. Cumberbatch (Claremont Graduate School), H. Ockendon (Oxford University)
I shall describe the modelling of a densiometer wihich first came to the CGU
Math Clinic and also a densitometer/viscometer which came to the UK Study
Group in 2002 (ESGI43). This reveals differences and similarities between
the modes of operation in the US and the UK as well as some interesting
modelling issues. The viscous treatment appeared unsatisfactory at first but
has been redeemed on closer analysis.
Some cracking ideas on egg incubation
N.C. Ovenden (University College London), C. M. Edwards (University of
Oxford), V. Rottschäfer (Universiteit Leiden)
The preservation of rare and endangered species of birds requires finding efficient, and above all successful, methods of breeding them in captivity. One
strategy adopted is to remove eggs from the mother, making her lay more
eggs, and then incubating the removed eggs artificially. Of course, artificial
incubation machines must attempt to replicate the conditions of natural incubation as closely as possible. Aside from careful control of temperature and
humidity within the artificial incubator, an important factor to replicate is that
eggs must be turned about their long axis from time to time. Hatching will
not occur in an egg that has not been subjected to some form of occasional
rotation. The reason why eggs are turned and the way in which they should
be turned are still not well understood.
The question of egg-turning was posed by Bristol Zoological Gardens and
investigated during the 46th European Study Group with Industry at the University of Bristol in spring 2003. During the week of the study group, we
attempted to gain some insight into why eggs have to be turned from a fluiddynamic perspective. The main questions we formulated and tried to answer
during the study group were the following:
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1. Why do birds rotate their eggs?
2. Does thermal convection play a role during incubation?
3. What are the properties of the flow inside the shell following an impulsive rotation?
4. Can the result be extended to eggs from different species?
5. How can we design better experiments using artificial eggs, to understand the birds’ behaviour during incubation?
We provide at least partial answers to all these questions and present a
simple egg-turning model, based on lubrication theory, for an egg in the initial
stages of incubation.
On the dynamics of a Bunsen flame
M.L. Bondar (Technische Universiteit Eindhoven), J.H.M. ten Thije
Boonkkamp (Technische Universiteit Eindhoven)
Common problems in domestic heating are instable combustion phenomena
and combustion associated noise due to the interaction between the flame and
the burner. Prediction and solving of acoustic instabilities requires a transfer
function that correlates the perturbations in the heat release rate and in the
gas velocity. The first step in deriving the transfer function for a given flame
velocity is solving of the G-equation. Using the method of characteristics,
we analytically solved the G-equation describing the dynamics of a Bunsentype flame under the assumption of Poiseuille gas flow. To overcome the
difficulties in obtaining a stationary flame using the method of characteristics, we have undertaken a numerical approach. For the stationary position
of the flame, our analytical-numerical results are consistent with the experimental data. Preliminary work on finding the transfer function which alows
prediction of acoustic instabilities will be discussed.
Solving the Maxwell equations for diffraction gratings with the C method
N.P. van der Aa (Technische Universiteit Eindhoven)
Diffraction gratings are often used in optical metrology. When an electromagnetic wave is incident on a grating, the periodicity of the grating causes a
multiplicity of diffraction orders. In many metrology applications one needs
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to know the diffraction efficiency of these orders. Since the period of a grating is often of the same order of magnitude as the wavelength, it is needed to
solve Maxwell’s equations rigorously in order to obtain these diffraction efficiencies. The C method (named after its inventor Chandezon) solves the local
Maxwell equations to obtain the desired far field. We will restrict ourselves
to a one-interface problem, which means that only two media are involved
separated by one interface. Another restriction is that diffraction gratings are
considered having a periodicity in only one direction. From ordinary diffraction theory it is known that above and below the grating grooves, one may
apply the Rayleigh expansions, since in those regions the material properties
(like the permittivity) are independent of the direction in which the grating is
periodic. The main characteristic of the C method is that it uses a coordinate
transformation to make the medium properties independent of the periodicity
direction for the entire domain, which implies that the Rayleigh expansions
can be used everywhere. The C method has the same starting-point as the
rigorous coupled-wave analysis (RCWA), which is another rigorous method
to compute the far field of a grating. This method is older and more widely
used. However, for a general interface description the C method has some
advantages compared to the RCWA algorithm, mainly related to speed and
accuracy.
High-order asymptotic approximation of three-dimensional fields within
thin thermo-elastic rods
O. Selsil (University of Liverpool), A.G. Aslanyan (MIREA), A.B.
Movchan (University of Liverpool)
This work presents an asymptotic algorithm for analysis of fields in thin thermoelastic rods of arbitrary cross-section under a general thermal load. The
approximation to the displacement field is derived in an explicit analytical
form. Boundary layers are also constructed near the ends of the rod, providing
valuable information for the completeness of the approximation. An illustrative example is given for the configuration used in an industrial application.
The analytical procedure described here enables one to obtain an accurate
approximation of displacement components and avoid heavy 3D numerical
computations. The resulting formula is new and has been used successfully
by engineers.
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The transfer of fibres in the carding machine
M.E.M. Lee (University of Southampton), H. Ockendon (University of
Oxford)
The problem of understanding the transfer of fibres between carding machine
surfaces is addressed by considering the movement of a single fibre in an
airflow. Particular attention is placed on understanding the aerodynamic flow
field which leads to insight into when fibres migrate between the different
process surfaces. In the case of a revolving-flats carding machine the theory
predicts a ‘strong’ aerodynamic mechanism between taker-in and cylinder
and a ‘weak’ mechanism between cylinder and doffer resulting in effective
transfer in the first case and a more limited transfer in the second.
Comparison of the Rigorous Coupled-Wave Analysis and Multiple Shooting
M.G.M.M. van Kraaij (Technische Universiteit Eindhoven)
Lithography often uses gratings for various metrology tasks such as alignment, overlay metrology and CD metrology. With the tightening requirements on metrology accuracy it becomes increasingly more important to understand the behaviour of the grating in the metrology application using a
rigorous mathematical diffraction model.
We present a well-known mathematical model based on the Rigorous
Coupled-Wave Analysis (RCWA) that can be used to solve optical diffraction
problems on periodic structures (both 1-D and 2-D gratings with approximated layer-structure). The algorithm calculates the reflected and transmitted
field which in turn determine the diffraction efficiencies for all reflected and
transmitted orders. This paper compares the RCWA method with a multiple
shooting method (also for the conical case) which is envisioned to further improve speed and robustness. It also provides a comparison with the theory in
[1].
Results created with a Matlab implementation of the RCWA algorithm
(MSolver) show excellent overlap with other published and measured data.
[1] Soon Ting Han, et. al, Electromagnetic scattering of two-dimensional surfacerelief dielectric gratings, Applied Optics 31(1992), 2343-2352
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Stability Analysis of a Pipe Conveying Fluid with Multifrequency Pulsatile Flow Velocity
L. Panda (Indian Institute of Technology), R.C. Kar (Indian Institute of
Technology), R. Mishra (Indian Institute of Technology)
This paper deals with a problem with wide implication in industries, mainly
the chemical and process industries. It investigates the stability of pipes
conveying an incompressible pulsating fluid with velocity which varies harmonically over a mean velocity constituting the parametric excitation for the
system. The excitation source has spectral content with multiple frequencies and arbitrary phases. The linear and non-linear equation of motion for
a simply supported pipe with pulsatile flow is considered. The analysis is
done by using the method of multiple scales (MMS) through direct perturbation method as well as by discretized-perturbation method and the results
obtained by both the methods are compared. Stability boundaries for primary
parametric instabilities, secondary instabilities and combination instabilities
are determined analytically through second order perturbation. The classical
result that primary instability occurs when one of the excitation frequencies
is close to twice a natural frequency changes as a result of multiple excitation
frequencies. Unusual interactions occur for the practically important case
of simultaneous primary and secondary instabilities. In non-linear analysis,
the non-linearity is introduced by including mid-plane stretching effect of the
pipe due to hinged end conditions. Amplitude-dependant non-linear frequencies are obtained. For frequencies close to two times the natural frequency,
stability and bifurcations of steady state solutions are analyzed.
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Thursday Morning
9:00–10:00
Plenary lecture
Multiphase and Multicomponent Flow in Porous Media in Industrial and
Environmental Applications (R. Helmig) . . . . . . . . . . . . . . . . . . 139
10:00–10:30
10:30–12:30
Mathematics in Electromagnetics (J.M.B. Kroot; theme: Electronic industry)141
Electromagnetic Field Computation and Noise Suppression in Particle-InCell Simulations (E. Gjonaj) . . . . . . . . . . . . . . . . . . . . . . . . 141
Analysis of Eddy Currents in a Gradient Coil (J.M.B. Kroot) . . . . . . . . . 142
Electromagnetic simulation methods for the design of Magnetic Resonance
Imaging equipment (J.A. Overweg) . . . . . . . . . . . . . . . . . . . . . 142
Time discretisations for staggered grid approaches (R. Horváth) . . . . . . . 143
Dynamic modeling of molten carbonate fuel cells (K. Chudej; theme:
Chemical technology) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
Development of a hierarchical model family for Molten Carbonate Fuel Cells
with Direct Internal Reforming (DIR-MCFC) (P. Heidebrecht) . . . . . . 144
Molten Carbonate Fuel Cell: Simulation and Optimization of a Partial
Differential-Algebraic Dynamical System (K. Sternberg) . . . . . . . . . 145
Nonlinear Model Reduction of a Dynamic Two-dimensional Molten Carbonate Fuel Cell Model (M. Mangold) . . . . . . . . . . . . . . . . . . . . . 145
Index analysis for singular PDE models of fuel cells (K. Chudej) . . . . . . 146
Financial and Insurance Mathematics (A. Bagchi; theme: Financial mathematics) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Multiplicative primal-dual bounds for Bermudan options (F. Jamshidian) . . 147
FX Instalment Options (U. Wystup) . . . . . . . . . . . . . . . . . . . . . . 148
Improved Estimators for Credit Risk Economic Capital and Economic Capital Contributions (E. Charlier) . . . . . . . . . . . . . . . . . . . . . . . . 148
Robust numerical methods for singularly perturbed multiscale flow problems I (J.M.L. Maubach; theme: Water flow) . . . . . . . . . . . . . . . 149
Comparison of adjoint equation approaches suitable for general purpose flow
solvers (G.F. Duivesteijn) . . . . . . . . . . . . . . . . . . . . . . . . . . 149
Iteration and preconditioning for indefinite systems (H.A. van der Vorst) . . 150
On the time integration of stiff advection-diffusion-reaction equations (J.G.
Verwer) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
BZ
H 11
H4
H 14
H 13
Thursday Morning
Multigrid and the discontinuous Galerkin method for convection-diffusion
equations (M.H. van Raalte) . . . . . . . . . . . . . . . . . . . . . . . . .
Novel Simulation Techniques for Unsteady Fluid Mechanics Problems
(J.J.W. van der Vegt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A multitime multigrid discontinuous Galerkin algorithm for vortex flow
around helicopter rotors (H. van der Ven) . . . . . . . . . . . . . . . . . .
A Space-Time Discontinuous Galerkin Method for Wet-Chemical Etching
(J.J. Sudirham) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Discontinuous Galerkin Method for Duct Acoustics (R. Hagmeijer) . . . . .
Implicit Subgrid-Scale Models in Space-Time Variational-Multiscale Discretisations (S.J. Hulshoff) . . . . . . . . . . . . . . . . . . . . . . . . .
The CAD-FEM Link (E.G. Quak) . . . . . . . . . . . . . . . . . . . . . . .
ViSiCADE - Bridging the Gap between CAD/CAE and VR (H. Graf) . . . .
Operators and criteria for integrating FEA in the design workflow: Toward a
multi-resolution mechanical model (J.C. Leon) . . . . . . . . . . . . . . .
Between a CAD model and a CFD mesh for ship geometries (V. Skytt) . . .
Contributed presentations (theme: Materials) . . . . . . . . . . . . . . . . .
Stochastic Approach to Simulation of Disturbances at Interfaces in Loaded
Heterogeneous Media (D.D. Moiseenko) . . . . . . . . . . . . . . . . . .
Shape Optimization of Curved Mechanical Structures (I. Tiba) . . . . . . . .
Multigrid Solution of Three-Dimensional Radiative Heat Transfer in Glass
Manufacturing (M. Seaid) . . . . . . . . . . . . . . . . . . . . . . . . . .
Determination of Interior Structure in Solids by Indirect Measurements
(A.A. Kharytonov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Liquid/solid phase change with convection and deformations: a 2D numerical test (D. Mansutti) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A mathematical model for mechanical etching of glass (J.H.M. ten Thije
Boonkkamp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
139
151
152
H5
152
153
154
155
155
156
H7
157
158
158 H 12
158
159
159
160
161
161
Multiphase and Multicomponent Flow in Porous Media in Industrial
and Environmental Applications
R. Helmig (Universität Stuttgart), H. Class, H. Jakobs
Thursday, 9:00–10:00, Blauwe Zaal
Water is of paramount social and economic value and its availability and use
will considerably influence the development of our societies. Therefore, a
sustainable management and protection of water in the environment is one
of the key tasks of the 21st century, and numerical modelling will contribute
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significantly to its solution. Models bridge the gap between domains and processes. They can simulate the complex flow and transport of several fluid
phases, e.g. water, Non-Aqueous Phase Liquids (NAPLs) and gas, and account for reactions between several chemical species, e.g. dissolved contaminants, nutrients. Within a hydro- or technical system, various relevant
processes occur within different subdomains. These relevant processes must
be considered on different space and time scales, and they require different
model concepts and data. First, some examples
• migration and storage of greenhouse gases in the subsurface
• atomic–waste–disposal sites
• subsurface remediation with steam injection
• multiphase processes in a fuel cell
will be used to demonstrate and motivate the necessity of coupling different model concepts and processes in the field of environmental and technical
problems.
For many multi-phase/multi-component systems, the exchange of chemical species between the fluid phases is crucial for the behavior of the whole
system because the flow of the phases is strongly affected by their composition.
Usually, the whole volume-coupled system is formulated for the entire solution domain. For such fully coupled systems, the same assumptions and
simplifications for the model concept have to be made for the whole system.
This leads to model concepts which include the whole complexity of all possible processes and phase states for the entire domain. As the phase state is
variable in space and time, for example, a computationally expensive threephase/three-component model must be chosen for the whole system even if
a less expensive single-phase/three-component model would be sufficient to
describe the relevant processes in wide areas of the system. To handle such
systems, an adaptive switch of the primary variables depending on the phase
state is necessary if a phase totally disappears in parts of the domain. Such
fully coupled model concepts for multi-phase problems result in large systems of strongly coupled nonlinear PDEs which have to be solved in the entire domain. Further, numerical schemes are often only suitable for parts of
the domain, depending on the dominant processes. A general overview of
different model concepts for multi-phase/multi-component systems will be
given.
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I shall present a number of different formulations for multiphase flow and
transport processes. It is very important to recognize the limitations and advantages of each formulation, e.g., the phase pressure formulation leads to
difficulties in the non–linear solver if both fluids are present at residual saturation in the domain.
Finally, this presentation will point out a number of critical problems and
limitations of the application of numerical models. Problems encountered by
extending single processes to coupled processes will be discussed.
Minisymposium: Mathematics in Electromagnetics
J.M.B. Kroot (Technische Universiteit Eindhoven)
Thursday, 10:30–12:30, Hall 11
Computations in electromagnetic fields can be executed in many different
ways, depending on the field of application. In circuit simulation for example,
the continuing trend of higher frequencies and smaller feature sizes, causes
significant electromagnetic effects on the interconnect, which cannot be neglected anymore. Therefore, a model of the behaviour of the interconnect
structures is needed. Other situations that require mathematical modelling are
for example radar systems, which are also high-frequent, and coils in MRIscanners, which can be both high-frequent and low-frequent. Analysis of the
model yields characteristics of the system and ways to reduce the order of the
model. In this symposium we present different mathematical methods used
in the area of electromagnetics, for both high-frequency and low-frequency
problems. Speakers are both from industry and from academia.
Electromagnetic Field Computation and Noise Suppression in ParticleIn-Cell Simulations
E. Gjonaj (Technische Universität Darmstadt), R. Schuhmann (Technische
Universität Darmstadt)
A review on recent developments in the electromagnetic field computation
for the simulation of charged particles with the Particle-In-Cell (PIC) technique will be given. Concentrating on particle-grid methods, we first compare
some of the most common approaches. Finite Integration (FIT) and FiniteDifference-Time-Domain (FDTD) methods show the highest efficiency and
can easily be scaled to cope with millions of unknowns on a standard PC. For
the accurate modelling of curved boundaries several conformal techniques
with submesh resolution are available. Finite Volume-type approaches, on
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the other hand, can be superior in terms of suppressing numerical noise, especially, when the interaction between electromagnetic fields and charged
particles is considered. Such a low dispersion method based on the upwindconservative discretization of the 3D-Maxwell’s equations in context of PIC
simulations will be presented. In the context of PIC simulations the application of this method benefits, additionally, from the higher regularity of the
particle-grid interpolation of the coupling currents.
Analysis of Eddy Currents in a Gradient Coil
J.M.B. Kroot (Technische Universiteit Eindhoven)
To provide the spatial information of MR images, the magnetic field strength
must show variation in space in a controllable manner. This variation is
provided by the three orthogonally positioned gradient coils, which produce
magnetic fields whose axial component varies linearly along all directions.
One of the major problems in the use of switched gradient coils is the interaction of the rapidly changing fields with other conducting structures in the MRI
scanner, including the gradient coils itself. Eddy currents are induced which
cause perturbations on the expected gradient field and, consequently, in the
MR picture, and should therefore be avoided as much as possible. The role of
eddy currents is important for Philips Medical Systems (PMS) for designing
gradient coils.
For the mathematical model, we consider a geometry of a finite number
of rings, which are considered infinitely thin. The rings have one common
central axis and are parallel. They have equal radii but different widths and
they are positioned at different mutual distances. The rings are not connected.
We can show that this is a specific model for the so called z-coil. The total
current through each of the rings is prescribed. However, the distribution of
the current is time- and space-dependent. The switching rate of a gradient
coil typically belongs to a low frequency range (in the order of kHz). Applying the theory of electromagnetic fields yields an integral equation for the
current distribution. We derive a solution for the current distribution in terms
of a series expansion of basis functions, the choice of which is based on the
characteristics of the kernel function.
Electromagnetic simulation methods for the design of Magnetic Resonance Imaging equipment
J.A. Overweg (Philips Research Laboratories Hamburg)
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A Magnetic Resonance Imaging (MRI) system comprises field generating
systems in the frequency range from 0 to 500 MHz. Many different electromagnetic simulation tools are required to simulate the various sub-systems.
Some design tasks can be done using standard, commercially available tools,
but other problems require dedicated tools. For the main field magnets the
design methods are usually nearly analytical. Automatic optimisation of the
magnet geometry is required to satisfy the homogeneity requirements (of the
order of a few parts per million). Similar quasi-static methods are used for
the design of the coils generating the switched gradient fields, which are operated at frequencies up to a few kHz. Gradient coil related eddy current effects
may be analysed using standard FEM tools. The radio-frequency transmit
and receive coils, which are operated at 10-500 MHz require the use of fullwave simulation tools. Optimisation of the coil geometry and tuning to the
proper frequency can best be done using boundary element methods. Analysis of the interaction with the patient (RF-heating effects) is preferably done
using FDTD methods, but depending on the required accuracy of the coil and
patient model, FEM tools can be an attractive alternative.
Time discretisations for staggered grid approaches
R. Horváth (University of West Hungary)
The Yee-method is a simple and elegant way of solving the time-dependent
Maxwell’s equations. On the other hand, this method has some inherent drawbacks too. The main one is that its stability requires a very strict upper bound
for the possible time-steps. This is why, during the last decade, the main goal
was to construct such methods that are unconditionally stable. This means
that the time-step can be chosen based only on accuracy instead of stability
considerations.
In this talk, using operator splittig methods, we give a uniform treatment of
methods that use the same spatial staggered grid approximation as the classical Yee-method. We discuss among others the Namiki-Zheng-Chen-Zhang
alternating direction implicit method (NZCZ) and the Kole-Figge-de Raedtmethod (KFR). We prove the unconditional stability of the NZCZ-method.
All methods are discussed with non-homogeneous material parameters.
Minisymposium: Dynamic modeling of molten carbonate fuel cells
K. Chudej (University of Bayreuth), M. Günther (Bergische Universität
Wuppertal)
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Stationary molten carbonate fuel cell stacks (MCFC) produce electrical
power in an enviromentally friendly way. Performance and service life of
MCFCs depends on its operating temperature. For higher temperatures material corrosion accelerates greatly, which shortens the stack lifespan. Therefore
control of the operation temperature within a specified range and reducing
temperature gradients are highly desirable.
Based on a family of newly developed hierachically ordered dynamic models – singular partial differential equation systems – of growing complexity
numerical simulations, parameter identifications, optimizations and optimal
controls will be presented in the four lectures. Model reduction via POD approaches will be presented in the second and third lecture. The last lecture
will present an analysis of a variety of indices of the varies singular partial
differential equation models as well as of the semidiscretised differentialalgebraic equation models.
Acknowledgement: The work of all 4 speakers is supported by the German
Federal Ministry of Education and Research within the project Optimierte
Prozessführung von Brennstoffzellensystemen mit Methoden der Nichtlinearen Dynamik.
Development of a hierarchical model family for Molten Carbonate Fuel
Cells with Direct Internal Reforming (DIR-MCFC)
P. Heidebrecht (University Magdeburg), K. Sundmacher (University Magdeburg)
Due to the manifold interactions of temperature field, electric potential and
reaction kinetics and due to several substantial and energetic back couplings,
molten carbonate fuel cells (MCFC) are complex technical systems. The integration of the fuel reforming process into the fuel cell, known as direct
internal reforming (DIR), not only offers an outstanding performance but it
also increases the systems complexity. In order to gain a deeper understanding of the interdependencies in a DIR-MCFC or to optimise the system design or to develop process control strategies, appropriate modelling is necessary. As each of these purposes requires different models with respect to
complexity, numerical solution effort and mathematical properties, the development of a whole model family is necessary. In this contribution, a detailed
reference model describing the transient behaviour of a spacially distributed
MCFC is introduced. The equations are based on the description of physical
and chemical processes and all system parameters are physically meaningful. The model itself proves to be rather complex to solve. Nevertheless, this
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model serves as a basis for the formulation of several further fuel cell models
for various purposes. As an example, the derivation of a simplified model is
demonstrated by applying minor physical simplifications. This model is used
in system optimisation and serves as a basis for further mathematical model
reduction. The derivation of a very simple steady state model, containing additional strongly simplifying assumptions, is shown. This model is suitable
for gaining elementary understanding of the system and for rough preliminary
system design.
Molten Carbonate Fuel Cell: Simulation and Optimization of a Partial
Differential-Algebraic Dynamical System
K. Sternberg (University of Bayreuth), K. Chudej (University of Bayreuth),
H. J. Pesch (University of Bayreuth)
The chemical energy of hydrogen is converted directly by fuel cells into electrical energy in a clean and highly efficient manner. We use a mathematical
model which is based on a molten carbonate fuel cell featuring a molten carbonate salt as electrolyte. This fuel cell produces the necessary hydrogen
from natural gas (methane) by an internal reforming reaction. Activated by
a catalyst, hydrogen molecules is converted into protons and electrons. The
electrons create a flow of electricity, while the protons move through the electrolyte and then react with oxygen.
The concentration, temperature and velocity of the involved substances in
the fuel cell are described by a system of partial differential equations. These
transportation equations simulate the plug flow and include the reaction kinetics of the substances. Furthermore, a heat exchange equation for the temperature in the solid phases of the fuel cell is used. Moreover the electrical
potentials are modeled by further differential and algebraic equations.
From a practical point of view we aim for a high electrical efficiency of
the fuel cell as well as for preventing the fuel cell from damage and material
abrasions due to large temperature gradients in the solid materials.
In this talk we will present numerical results for the optimized problem and
we will discuss the behavior of the plug flow and the temperature changes of
a time dependent two dimensional model of the molten carbonate fuel cell.
Nonlinear Model Reduction of a Dynamic Two-dimensional Molten Carbonate Fuel Cell Model
M. Mangold (Max-Planck-Institut Magdeburg), M. Sheng (Max-PlanckInstitut Magdeburg)
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The control of the spatial temperature profiles is an important point for the operation of high temperature fuel cell stacks. The simulation and prediction of
the temperature gradients requires mathematical models described by partial
differential equations with up to three space coordinates. The dynamic numerical solution of such spatially distributed models is time consuming. For
process control purposes, e.g., the design of advanced feedback controllers
or optimization problems, nonlinear spatially distributed models are often too
complicated. Simplified or reduced models are desirable that give a good approximation of the original model’s solution for a certain range of operation
conditions. In this contribution, the Karhunen Loéve Galerkin procedure is
used to derive a reduced model from a spatially distributed model of a molten
carbonate fuel cell (MCFC).
In order to obtain a reduced model of the cell, the Galerkin procedure of
weighted residuals is applied to a dynamic spatially two-dimensional model.
The spatial basis functions for the Galerkin method are generated from numerical simulation results of the distributed model. The resulting reduced
model is a low order differential algebraic system of index one. Simulation
studies show a good agreement between the reduced model and the reference
model. Although the basis functions are obtained from numerical test simulations, the reduced model possesses good extrapolation qualities. Compared
with the complete model, the computation time is reduced by a factor of up
to 100. This qualifies the reduced model for real-time applications like model
based control strategies.
Index analysis for singular PDE models of fuel cells
K. Chudej (University of Bayreuth), M. Gnnther (Bergische Universität
Wuppertal)
During the last two years a hierarchy of 1D and 2D singular PDE models
were developed by Heidebrecht & Sundmacher, which describe the dynamic
behaviour of molten carbonate fuel cells.
In order to determine correctly formulated initial and boundary conditions
of these singular PDEs generalizations of previously introduced spatial and
time (differential) indices are necessary. These (differential) indices of the
singular PDE are computed via a new approach using integral equations. The
singular (1D) PDE is numerically solved by the method of lines (MOL),
which yields after semi-discretization a differential-algebraic equation (in
time). The differential index of this semi-discretized problem is called MOL
index and is related to the (differential) time index of the singular PDE.
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From a numerical point of view perturbation indices are more important.
The relationship between the perturbation index and the differential index
(MOL index) of the semi-discretized problem is well known. The computation and definition of perturbation indice for singular PDEs is an active
research area: We present new results on perturbation indices of linearized
singular PDE models of fuel cells.
We will close with some results of numerical computations.
Minisymposium: Financial and Insurance Mathematics
A. Bagchi (University of Twente)
In this minisymposium current developments in financial and insurance mathematics will be discussed. Stochastic analysis will be the underlying theme
throughout. The lectures will cover pricing issues, computational questions
for multi-dimensional options, credit risk and reinsurance problems. The lectures will be complementary and delivered by a group of renouwned international experts with considerable practical experience. Applicability of the
proposed methods will be the key focus of the talks. Mathematical topics that
will play major roles in the talks include: Monte Carlo simulation, primaldual method, stochastic optimization and rare event distributions. Simulation
and optimization will be the recurring themes throughout, and the lectures are
expected to motivate the uninitiated to take a closer look into this recent field
of financial engineering.
Multiplicative primal-dual bounds for Bermudan options
F. Jamshidian (NIB Capital Bank)
Given an exercise strategy, the primal-dual method provides simultaneously
a lower bound and an upper bound for the price of a Bermudan option. The
additive version of this method was developed in [A-B] and further studied
in [K-S]. It utilizes the additive dual representation of American and Bermudan option developed in [R] and [H-K]. This presentation describes a new
multiplicative version of the primal-dual method. The multiplicative version
enjoys an intuitive financial interpretation, as all constructs are deduced from
arbitrage argument and self-financing trading strategies.
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FX Instalment Options
U. Wystup (HfB - Business School of Finance and Man), S. Griebsch
(Goethe University), C. Kühn (Goethe University)
We explain the importance and practical applications of instalment contracts
in the FX options OTC market. Next we present a survey of pricing techniques that can be used to price and risk manage this exotic option. This will
include nested numerical integration, binomial trees, a dynamic programming
approach and partial differential equations. In the Black-Scholes model we
have derived a closed-form solution, which to our belief has not been published before. Under this model, we show how to implement it and test the
performance of the various pricing techniques for convergence, stability, practicality and speed. In many cases the pricing can be transferred to more general models. We also outline a model independent hedging strategy and show
how the instalment option converges to a certain type of American option
with a time-dependent strike price as the number of decision days increases.
This allows to approximate the n-dimensional instalment integral by a simple binomial tree based product. This is joint work with Susanne Griebsch
(Goethe University) and Christoph Kühn (Frankfurt MathFinance Institute).
Improved Estimators for Credit Risk Economic Capital and Economic
Capital Contributions
E. Charlier (ABN AMRO Bank), K. Veltman (Tilburg University)
Economic Capital and Economic Capital contributions play an important role
within financial institutions. Within a credit portfolio Economic Capital is the
amount of money a financial institution has to hold on this portfolio above the
expected portfolio loss as a buffer against unforseen credit losses. Besides the
credit risk at portfolio level there is also interest in calculating the contribution
of each single credit facility to the portfolio EC. This is called Economic
Capital Contribution.
We discuss improved estimators based on an Importance Sampling transformation. Importance Sampling (IS) is a technique widly applied to reduce
the variance of estimators in general. The object in IS is to concentrate the
distribution of the sample points in the parts of the distribution that are of most
‘importance’ instead of simply drawing randomly. Within a credit risk setting
most ‘important’ are extreme portfolio losses from which a high quantile is
estimated.
For the estimation of Economic Capital we focus on a transformation of
the mean of the driving factor returns and on a transformation of the indi-
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vidual default probabilities. This will allow us to simulate more losses near
extreme quantiles in general. Also Extreme Value Theory is used to estimate
extreme quantiles. For the estimation of Economic Capital Contributions we
only change the driving factor returns. The IS transformations proposed to
estimate Economic Capital and Economic Capital Contributions are tested on
stylised portfolios. Results show that the variance of the estimators is reduced
significantly.
Minisymposium: Robust numerical methods for singularly perturbed
multiscale flow problems I
J.M.L. Maubach (Technische Universiteit Eindhoven)
The study of many theoretical and applied flow problems in science and technology leads to boundary value problems of singularly perturbed partial differential equations that have a multiscale character. Thus, it is of considerable
scientific interest to develop a solid mathematical theory and specific computational methods for singularly perturbed multiscale problems and related
problems arising from applications. The design of robust numerical methods
for such problems, i.e. methods whose accuracy does not depend on local
scales of singular components of the solution, is an important task. The symposia I and II will discuss numerical methods for convection diffusion equations, related iterative solution methods and also numerical methods for more
complex flow problems. Invited speakers refer to each others approaches.
The contributions are in part supported by N.W.O. grant 047.016.008.
Comparison of adjoint equation approaches suitable for general purpose
flow solvers
G.F. Duivesteijn (Delft University of Technology), H. Bijl (TU Delft), B.
Koren (TU Delft)
For computation of complex aerospace engineering problems, an efficient error estimation and grid adaptation algorithm is highly desirable. However,
traditional error estimation and grid adaptation do not suffice, since they are
insufficiently related to relevant engineering variables. The dual formulation
can be used in the a-posteriori error estimation for the quantity of interest.
However, derivation and solution of the dual problem, especially the accompanying boundary conditions, is not a trivial task, with which the user of a
general purpose flow solver cannot be burdened. In this paper, formulations
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and implementations for adjoint based adaptation are investigated. Special attention is given to the automatic derivation of a well-posed dual problem. To
begin with, there are two ways to formulate the dual problem: analytical and
discrete. This paper gives a rapid review of the analytical dual problem and
the derivation of boundary conditions for the discretized analytical dual solution method will be explained. Next, the discrete dual solution problem will
be discussed. Imposing strong or weak boundary conditions for the primal
problem has a great influence on the implicitly given boundary conditions of
the numerical dual problem. Also, dependency of the dual solution related to
the chosen flux evaluator in the primal solution will be discussed. There are
three techniques to evaluate the Jacobian, needed for setting up the dual problem. For the analytical dual formulation, differentiation is done by hand or
with aid of a symbolic mathematical software program. For the discrete dual
problem, differentiation can be done by divided derivatives or with automatic
differentiation. Both methods will be compared and discussed.
Iteration and preconditioning for indefinite systems
H.A. van der Vorst (Utrecht University)
The hope to find a general robust preconditioner for suitable iterative methods
for various indefinite linear systems seems to be idle. However, for special
classes of linear systems successes have been reported. In our presentation we
will highlight some preconditioners and the ideas behind them. These preconditioners have been motivated by systems coming from CFD problems, electric circuit simulation, and eigenvalue computation with the Jacobi-Davidson
method.
On the time integration of stiff advection-diffusion-reaction equations
J.G. Verwer (CWI, Amsterdam)
Time integration of stiff, large-scale advection-diffusion-reaction equations
by means of standard Runge-Kutta and linear multistep methods is often
not feasible due to efficiency or memory restrictions. We discuss a special
method of Runge-Kutta-Chebyshev type, which handles advection and diffusion terms explicitly and stiff reaction terms implicitly. Assuming finitevolume or finite-difference spatial discretization, this RKC method handles
moderately stiff diffusion terms efficiently due to stabilization by the threeterm Chebyshev recursion. Advection terms can be treated with CFL numbers
common for explicit methods assuming upwind discretization. Stiff reaction
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terms pose no stability step size restrictions at all provided reaction Jacobians possess real eigenvalues. For PDE systems with many components and
highly expensive chemistry, it is easy to use paralellization because the chemistry computation is completely decoupled over the grid when finite-volume
or finite-difference spatial discretization is used.
[1] J.G. Verwer, B.P. Sommeijer (2003), An implicit-explicit Runge-KuttaChebyshev scheme for diffusion-reaction equations. Report MAS-R0305,
preprint CWI (see www.cwi.nl/˜janv), to appear in SIAM J. Sci. Comput.
[2] J.G. Verwer, B.P. Sommeijer, W. Hundsdorfer (2004), Incorporating avection in
the Runge-Kutta-Chebyshev method, in preparation.
Multigrid and the discontinuous Galerkin method for convection-diffusion
equations
M.H. van Raalte (CWI, Amsterdam), P.W. Hemker (CWI, Amsterdam)
In this talk we discuss multigrid iteration for the solution of the linear convection-diffusion equation, discretized by a discontinuous Galerkin
method. In particular we study the convection-diffusion case where possibly
the inverse cell-Reynolds number is smaller than one.
We motivate our choice for the Baumann-Oden (BO) and for the Nonsymmetric Interior Penalty (NIPG) discontinuous Galerkin method. We show
the structure of the discrete operator and we distinguish between cell-wise and
point-wise block-relaxation methods.
By Fourier analysis, we show for the BO-method that, in case of dominating diffusion, most point-wise block-relaxation smoothers yield very efficient multigrid algorithms. However, for dominating convection and pure
convection, acceptable MG convergence can only be expected if point-wise
block-Jacobi smoothing is applied and the problem is solved with sufficient
accuracy on the coarser mesh.
On the other hand, MG with classical cell-wise symmetric Gauss-Seidel
smoothing is quite effective for the NIPG method and convergence factors
ρ < 0.3 can be expected for the the whole range from diffusion, convectiondiffusion to pure convection. Moreover, an analysis of the two-level spectral
norm shows that an reduction in the residue is guaranteed within two iteration
steps.
The present analysis justifies the use of an interior penalty term in higher
order DG-methods, when MG is applied for the solution of the convectiondiffusion equation.
The presentation is given by P.W. Hemker.
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Minisymposium: Novel Simulation Techniques for Unsteady Fluid
Mechanics Problems
J.J.W. van der Vegt (University of Twente)
In this minisymposium we will discuss some novel techniques which promise
significant improvements for the simulation of unsteady flows.
An important class consists of discontinuous Galerkin finite element methods, which are well suited for hp-adaptation due to their local element based
discretization. An interesting new class of DG methods is the space-time DG
method, which uses discontinuous basis functions, both in space and time,
and results in a conservative discretization for problems with time-dependent
boundaries. Two important applications which will be discussed are the simulation of the unsteady flow about helicopter rotors in forward flight and the
motion of an etching cavity boundary during a wet chemical etching process.
The combined discretization in space and time also offers the possibility to
significantly improve the computational efficiency using a multi-time multigrid algorithm.
Discontinuous Galerkin methods are also well suited for problems which
require higher order accuracy and the application of DG methods to acoustics
will be discussed with special emphasis on the analysis of the accuracy of
acoustic waves in a DG discretization.
At high Reynolds numbers it is, however, not possible to compute all relevant scales and an important new technique is provided by the variational
multiscale method. This method has close links with large eddy simulation,
but offers considerable flexibility, in that the local mesh size, interpolation
basis, and partitioning between scales with and without physical SGS models can be varied. The effects of each of these discretization options on the
response of implicit SGS models is analysed, and the implications for the
implementation of physical SGS models are discussed.
A multitime multigrid discontinuous Galerkin algorithm for vortex flow
around helicopter rotors
H. van der Ven (Netherlands National Aerospace Laboratory), O.J. Boelens
(Netherlands National Aerospace Lab.)
To improve pilot and passenger comfort and to reduce the service hours on the
ground, a good understanding of the origin of the vibrations in a helicopter
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is required. These vibrations are caused by an intricate interaction between
structural dynamics and aerodynamics.
The basic idea of the four-dimensional solution algorithm [1] is that a
time-periodic problem can be considered a steady problem in the sense that
after one time period the next period shows the same phenomena. This is
formalised by solving the time-dependent equations simultaneously in both
space and time for the complete period of the problem. The equations are
solved on a four-dimensional space-time grid.
The main advantage of the solution algorithm lies in the fact that it transforms a time-dependent problem into a steady-state problem. This has several
advantages:
• the final solution is independent of the solution process;
• local grid refinement can be extended to the time dimension;
• no dynamic load balancing problems on parallel machines;
• time-accurate coupling with other physics models is straightforward.
These four points show that the solution algorithm is excellently suited for
aeroelastic simulations of rotor systems in forward flight. The aeroelastic
coupling, the rotor trimming procedure, and the local grid refinement process
for improved vortex capturing are combined in an elegant way, without one
of the processes jeopardizing the efficieny of the other processes.
At the presentation, results for an aeroelastic simulation of the four-bladed
BO105 +M296 rotor in forward flight will be shown.
[1] H. van der Ven and O.J. Boelens. Towards affordable CFD simulations of rotor in
forward flight - a feasibility study with future application to vibrational analysis,
59th AHS Forum, Phoenix, USA, May 6-8, 2003.
A Space-Time Discontinuous Galerkin Method for Wet-Chemical Etching
J.J. Sudirham (University of Twente), J.J.W. van der Vegt (University of
Twente), R.M.J. van Damme (University of Twente)
Wet-chemical etching is a manufacturing technique which is well suited for
the machining of complicated small devices. An etching fluid is used to dissolve the material, while the rest of material is protected by an impenetrable mask. This technique is attractive for micromachining, because it is a
fast room temperature process and the production process is independent of
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the complexity of the design. The control of the etching process is, however, not fully understood. This results in inacccuracies in the product of the
etching process. In order to improve the understanding of the wet-chemical
etching process, there is a strong need for accurate mathematical models. Recently, we have developed a space-time discontinuous Galerkin finite element
method for parabolic problems with moving boundaries. In this presentation
we will summarize the finite element discretization and discuss the modelling
of the transport of the etching fluid concentration, which we assume is governed by an advection-diffusion equation. The finite element method is adaptive, therefore it is well suited for the wet-chemical etching process, as the
behaviour of the process requires the accurate capturing of the silicon-etchant
interface, thin boundary layers and corner singularities. As an example, we
apply the method to etching of a slit and the results are compared with analytic studies and other numerical experiments.
Discontinuous Galerkin Method for Duct Acoustics
R. Hagmeijer (University of Twente), C.P.A. Blom (University of Twente),
H. Ózdemir (University of Twente)
The present paper deals with the analysis of duct acoustics by means of the
Discontinuous Galerkin finite element method. It summarizes part of the
work done within two research projects at our department [1], [2]. The industrial problem considered is that of acoustic radiation from a vibrating wall
segment inside an infinite rectangular duct. The objective is to compare numerical with analytical results in order to identify the relevant phenomena
and to verify the numerical algorithms employed.
We employ the Discontinuous Galerkin (DG) finite element method. The
currently used implementations are upto fourth order accurate in space and
time. We use tetrahedral [1] or hexahedral [2] elements.
We present detailed analytical solutions for two specific cases: (i) plunging
rigid wall segment, and (ii) an harmonically deforming (in space and time)
wall segment. All of the analytical work presented is taken from [1].
We have obtained good agreement between analytical and numerical solutions, although evaluation of the analytical results is a challenge in itself.
Due to the large number of integrals over infinite domains that have to be
calculated, we have therefore, at various stages, taken the leading term only.
It appears that these leading term already captures most of the characteristics
of the solution.
[1] C.P.A. Blom, Discontinuous Galerkin Method on Tetrahedral Elements for
Aeroacoustics, Ph.D.-thesis, University of Twente, September 2003.
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[2] H. Ózdemir, Discontinuous Galerkin Method on Hexahedral Elements for
Aeroacoustics, Ph.D.-thesis, University of Twente, in progress.
Implicit Subgrid-Scale Models in Space-Time Variational-Multiscale
Discretisations
S.J. Hulshoff (Delft University of Technology)
The premise of large-eddy simulation (LES) is to compute only the largest
scales of a turbulent flow, while representing the effects of unresolved scales
using a physical subgrid-scale (SGS) model. Typically such models attempt
to account for turbulent energy dissipation, which in high-Reynolds-number
flows occurs at wave numbers far higher than are practically resolvable.
Inherent to numerical methods for LES, however, are discretization errors
which are greatest in magnitude for the smallest resolved scales. These errors
combine to produce an implicit SGS model for the effects of the unresolved
scales. We examine the behavior of implicit sub-grid scale (SGS) models introduced by space-time variational-multiscale discretisations. We limit our
attention to time-discontinuous formulations, which are advantageous in that
they allow arbitrary re-meshing between time steps. For clarity, we consider
discretizations for the viscous Burger’s equation. As application of the timediscontinuous approach introduces secondary unknowns related through a
system of non-linear equations, traditional modified-equation approaches for
estimating the implicit SGS model cannot be applied. We consider instead
linearised approximations, and examine their fidelity by comparison with numerical experiment. The variational-multiscale approach offers considerable
flexibility, in that the local mesh size, interpolation basis, and partitioning
between scales with and without physical SGS models can be varied. The
effects of each of these discretization options on the response of implicit SGS
model is analysed, and the implications for the implementation of physical
SGS models are discussed.
Minisymposium: The CAD-FEM Link
E.G. Quak (SINTEF ICT)
The simulation phase during a product development process is expanding in
order to reduce the product development cycle time. Simultaneously an increasing number of physical phenomena are addressed through simulation
models. Providing suitable input for such numerical simulations is known to
be a rather time-consuming process.
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Design models (BRep - NURBS type models) produced by CAD systems
or digitised models often contain cracks or are far too complicated to be fed
into a simulation package directly. Thus such models have to be adapted
before they can serve as the input for numerical simulation, typically necessitating a lot of human interaction. In the other direction, the results of a
simulation should trigger a shape adaptation process and allow the reuse of
existing models and model interoperability.
The aim of this mini-symposium is twofold. One goal is to discuss developments concerning the CAD-FEM link from the recent work of the contributors. On the other hand we wish to present this subject as one of the
research tasks addressed by the newly established EU IST Network of Excellence AIM@SHAPE, addressing topics concerned with the semantics of
shapes: Advanced and Innovative Models and Tools for the Development of
Semantic-based systems for Handling, Acquiring and Processing Knowledge
Embedded in multidimensional digital objects, started January 2004 in the
Key Action ”Semantic-based knowledge systems”.
ViSiCADE - Bridging the Gap between CAD/CAE and VR
H. Graf (Fraunhofer Institute for Computer Graphics)
Due to the increasing availability of high performance computing hardware
more complex and realistic simulations can be run in shorter time periods.
As such computations and measurements mostly result in large sets of scalar
or vector data, appropriate visualization tools are required for a proper analysis, interpretation and presentation. An engineer is, e.g. interested in the
behaviour of a flow field around a car without having to lead expensive tests
in a wind channel. Nevertheless, such computations are in general very time
consuming and are either performed on massive parallel high performance
clusters or shifted into a pre-processing step to achieve simpler but more accurate analysis models. Different VR based solutions and research applications have been published in order to enhance the analysis stage. However,
those target common post processing techniques rather than supporting engineers during model preparation, analysis and simulation. Though, VR based
solutions could increase the efficiency during the analysis stage providing
a highly reactive environment in which an engineer is able to work within
one environment accomplishing CAD model preparation, e.g. feature detection and removal, interactive mesh refinement and real-time simulation on
submodels. ViSiCADE offers an innovative solution based on a distributed
platform combining CAD model preparation, CAE model generation, interactive mesh refinement strategies and real-time analysis on smaller submodels.
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This methodology aims at a rapid analysis step in which the engineer is able
to identify critical regions allowing him to judge where to spend his analysis time and re-simulate the areas of interest on refined simulation problems.
Hence, the developed techniques allow to accomplish analysis tasks more
quickly saving time for the overall analysis stage and leading faster ‘what-if’
analysis.
Operators and criteria for integrating FEA in the design workflow: Toward a multi-resolution mechanical model
J.C. Leon (Laboratory Soils, Solids, Structures (3S), P. Marin (Laboratory Soils, Solids, Structures (3S), G. Foucault (Laboratory Soils, Solids,
Structures (3S)
Efficiently integrating the Finite Element Analysis (FEA) process into the
design workflow requires a capability of the FEA task to cope with a wide
variety of input models. Therefore, the FEA process should be able to accept
as input the corresponding variety of models (CAD, digitized, pre-existing FE
models). Here, the approach described is based on a concept of intermediate
polyhedral model as a mean to handle all these configurations. Component
or system shape changes required by the FEA process need to be governed
by mechanical criteria. Two different categories shape adaptation process can
be faced: a priori and a posteriori. The first one illustrates the prominence of
the engineer’s know-how to perform the shape changes whereas the second
one is pragmatic and based on FE error estimators applied after a first rough
resolution process. Hence, different categories of criteria are required to monitor the shape changes during the shape adaptation process: estimates of the
distribution of the field values (displacements, temperatures, stresses, ?), volume, surface or inertia variations, ? The incorporation of these criteria is the
second aspect that is illustrated through the approach described. The way the
above criteria are applied involve a data transfer mechanism during the shape
adaptation process. Such a mechanism can be associated with constraints to
express the appropriate concepts like preserving the resultant force for boundary conditions. Combining the constraints and transfer process leads to the
concept of multi-resolution mechanical model that is introduced to characterize the capability of this mechanism to provide a consistent mechanical model
at each step of the shape changes required when preparing a FEA. In addition,
it will illustrated how this concepts can be also applied to FE simulation results and produce compact visualization models that are easier to disseminate
for collaborative purposes like Digital Mock-Up reviews.
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Between a CAD model and a CFD mesh for ship geometries
V. Skytt (SINTEF)
Fantastic and Leading Edge are two EU projects aimed at developing methods for producing good design for ship hulls and propellers, respectively. An
important tool in this context is CFD simulations based on a given geometry model. However, a CAD model representing the geometry and a model
suited for CFD calculations are different in nature. A CAD model consists of
surfaces representing the object with a lot of details, and where the various
surfaces may meet with continuity defined within some tolerance. A model
fit for CFD will be a mesh where some details may be omitted, but where the
continuity between adjacent elements in the mesh is exact. The talk will emphasize the transition from a CAD model to a CFD model for this particular
type of applications.
Contributed presentations (theme: Materials)
Stochastic Approach to Simulation of Disturbances at Interfaces in
Loaded Heterogeneous Media
D.D. Moiseenko (ISPMS Siberian Branch Russian Academy of Sciences),
P.V. Maksimov (ISPMS SB RAS)
For a long time it was usual to describe residual stresses in deformed solids
from the viewpoint of previous evolution of deformation fields. Most of traditional mechanics approaches were based on the implicit assumption of existence of certain ‘deterministic’ laws prescribing the change of the strain
fields. However, it is evident that structure transformations taking place in
heterogeneous media are essential for all of material properties. In the last
years stochastic approach seems to be very perspective due to its ability to
take into account real peculiarities of media behavior as it can be observed in
direct experimental research. In the present study an algorithm for stochastic
generation of interface disturbances in heterogeneous media is proposed. Initial parameters of the model here are total length of interfaces between structure domains L, total number of domains P, their minimal size d, minimal
interface thickness D and different kinds of local ‘microproperties’, which
describe interactions between the structure elements. Interfaces of loaded heterogeneous media represent a set of curves. The form of each curve depends
on basic functions, which describe interaction peculiarities. In the framework of the stochastic model the parameters of these basic functions are
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random variables. The expected values of these variables characterize ‘intensity’ of processes and statistical dispersion is some kind of dissipation rate.
In the present study simulation of ‘spatial oscillatory’ feature of deformation
along interfaces between neighboring structure domains is carried out. The
results of the study show that during the loading, at each time step, further
stress concentrators of different size and intensity are generated and spatial
distribution of the concentrators has quasiperiodic ‘oscillatory’ character. The
study demonstrates ability of proposed approach to grade stress concentrators
by their scale. It allows to simulate generation of dislocations, disclinations
and cracks at the interfaces in heterogeneous media.
Shape Optimization of Curved Mechanical Structures
I. Tiba (Weierstrass Institute, Berlin)
We consider structures like arches, curved rods and shells for which we
study new existence and regularity properties. We also present numerical
approaches and numerical experiments for certain applications. In the optimization problems the unknown is the shape of the structure, indicated via
appropriate parametrizations. It is assumed that a prescribed field of forces
acts on any of the admissible bodies that we study and the performance index
is of integral type. The minimization of this functional is related to ensuring a
‘desired’ deformation response of the (unknown) body under the action of the
given forces. Our results concern existence of optimal structures, sensitivity
analysis and numerical methods. Several computed examples with physical
relevance are also included.
Multigrid Solution of Three-Dimensional Radiative Heat Transfer in
Glass Manufacturing
M. Seaid (Technische Universität Darmstadt), A. Klar (TU Darmstadt)
Developing efficient and accurate techniques to solve radiative heat transfer
attracts many researches from several applications as, radiation hydrodynamics, combustion, or glass manufacturing. In this later field, Rosseland approximation could be the most cheap (as far as the efficiency is concerned)
solution for such equations. However, this approximation fails to resolve accurately the boundary layers in the cooling processes. In non-diffusive limits
(optically thin material) only the solution of the full radiative heat transfer
can provid high quality products.
In our contribution, we present a new algorithm to approximate the full radiative heat transfer problem. The algorithm consists of linear and nonlinear
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multigrid techniques. Thus using the same mesh hierarchy for both radiative
transfer and heat conduction, the linear system arising from the discretization of radiative transfer is solved by multilevel method using the AtkinsonBrakhage approximate inverse as a preconditioner. On the other hand a multilevel solver, using Newton-Krylov as a smoother, is used for the discretized
heat conduction. In both methods linear systems are solved only on the coarse
mesh.
Numerical investigations (robustness, efficiency and convergence rates) are
carried out in a three-dimensional problem. Special attention is given to an
eight frequency bands model kindly provided by ITWM in Kaiserslautern.
Comparisons to other methods and the sensibility of the algorithm on ordinate
and space discretizations are also discussed in our contribution.
Determination of Interior Structure in Solids by Indirect Measurements
A.A. Kharytonov (University of Kiel)
We propose to consider the following inverse problems for the determination
of the interior structure in materials.
1. The elastic solid has holes or cracks. We shall assume that all holes
have one form and orientation but various size. Let c be the apparent length
scale of the hole and ϕ(c) is the hole size distribution function for the noninteracting approximation. If the elastic body is acted upon by a uniform
stress p0 , the variation of strain energy due to the presence of holes W ( p0 )
and the unknown function ϕ(c) one can connect by the integral equation
Z cmax
K ( p0 , c)ϕ(c)dc = W ( p0 ).
(11.1)
cmin
Here the kernel K ( p0 , c) is the known function from elasticity theory.
2. Consider some porous solid. We assume that the porous medium consists of cavities or pores of different size. The pore radius R is defined as the
radius of a sphere which has a volume equal to the pore volume. The adsorption process in the porous solid can be described by the following Fredholm
integral equation of the first kind
Z Rmax
K (P, R)y(R)d R = f (P).
(11.2)
Rmin
Here f (P) is the adsorption isotherm, which is known from experiments as a
function of the pressure P; y(R) is the unknown pore size distribution function. Numerical experiments with the Tikhonov regularization method illus-
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trate the capabilities and efficiency of this methodology.
Liquid/solid phase change with convection and deformations: a 2D numerical test
D. Mansutti (C.N.R.), R. Raffo (C.N.R.), R. Santi (C.N.R.)
In recent experiments of melting of pure metals [1], the hypothesis has been
raised that the convection flow within the liquid phase might be responsible
for the structural variations in the solid portion close to the phase interface.
The nature of such processes indicate that mathematical and numerical assessments are necessary.
Recently, a mathematical model has been built for liquid/solid phase transitions capable to describe the dynamics of the liquid and solid phases (velocity
field of the liquid and deformation field of the solid), the heat transport phenomena and the evolution of the phase front [2]. This model has been already
adopted to reproduce the solidification of a water layer and provided results
in excellent agreement with the analytical solution [3].
Here we face a 2D test case. In order to accomplish this aim, the mathematical model has been reformulated with the use of potential functions allowing
to meet more easily the incompressibility constraint. We chose to simulate
the melting experiment of a pure gallium slab heated on a side described by
Gau & Viskanta in [4].
We shall discuss the results of the present simulation versus those ones
previously obtained by one author without deformation effects [5].
[1] P. Gondi, R. Montanari, E. Evangelista, G. Buroni. Microgravity Quarterly,
7(4):155-173, 1997.
[2] F. Baldoni. Thermomechanics of solidification. Pittsburgh University Press,
1997.
[3] D. Mansutti, F. Baldoni and K. R. Rajagopal. Mathematical Models & Methods
in Applied Sciences. 11(2):367-386, 2001.
[4] C. Gau and R. Viskanta. Transaction of the ASME. 108:174-181, 1986.
[5] M.M. Cerimele, D. Mansutti and F. Pistella. Computers and Fluids. 31:437-451,
2002.
A mathematical model for mechanical etching of glass
J.H.M. ten Thije Boonkkamp (Technische Universiteit Eindhoven)
Mechanical etching of glass by powder blasting is a technique to pattern glass
plates with small circular holes. In this talk we derive a nonlinear first order
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PDE describing the displacement of the glass surface. This equation is solved
both analytically, using the characteristic-strip equations, and numerically,
using level set methods. The results are compared with measurements.
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Thursday Afternoon
13:30–14:30
Plenary lecture
Mathematical modelling of industrial flow processes with complex boundaries (J. Hunt) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
14:30–15:00
15:00–17:00
Electronic transport in semiconductor devices (L.L. Bonilla; theme: Electronic industry) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A deterministic multicell solution to the coupled Boltzmann-Poisson system
simulating the transients of a 2D silicon MESFET (C. Ertler) . . . . . . .
Stochastic kinetic and drift-diffusion equations describing shot noise in miniband semiconductor superlattices (G. Dell’Acqua) . . . . . . . . . . . . .
Quantum kinetic and drift-diffusion equations for semiconductor superlattices (L.L. Bonilla) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Hydrodynamic transport models for an ultra-thin base Si Bipolar Transistor.
(M. Muscato) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Domain Displacements and Ramping Time in Superlattices (B. Birnir) . . .
Robust numerical methods for singularly perturbed multiscale flow problems II (J.M.L. Maubach; theme: Water flow) . . . . . . . . . . . . . . .
On Massively Parallel Finite Element Methods for Convection-Diffusion
Problems (J.M.L. Maubach) . . . . . . . . . . . . . . . . . . . . . . . . .
Local defect correction with compact finite difference schemes for convectiondiffusion equations (M. Sizov) . . . . . . . . . . . . . . . . . . . . . . .
A Fully Conservative Model for Compressible Two-Fluid Flow (J. Wackers)
Two-Phase Simulations of Water Waves in the Offshore Industry (R. Luppes)
Analysis of a multigrid method for convection-diffusion problems (M.A. Olshanskii) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Combustion Simulation (J.H.M. ten Thije Boonkkamp) . . . . . . . . . . .
An exponential scheme for the numerical simulation of laminar flames
(J.H.M. ten Thije Boonkkamp) . . . . . . . . . . . . . . . . . . . . . . .
Local Defect Correction for Laminar Flame Simulation (M. Graziadei) . . .
The Phase-Space Intrinsic Low-Dimesional Manifold method to reduce
chemical kinetics (H. Bongers) . . . . . . . . . . . . . . . . . . . . . . .
Regularization modeling of turbulent flames (B.J. Geurts) . . . . . . . . . .
Contributed presentations (theme: Aerospace) . . . . . . . . . . . . . . . .
166
BZ
H 11
167
167
168
168
169
169
H 13
170
170
171
171
172
173
H7
174
174
174
175
175 H 5
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Mathematical Modeling of Plasma and Sheath (N. Sternberg) . . . . . . . . 175
Unsteady Heat Load Reduction at the Reentry of a Future Mars Express Capsule (R. Callies) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Optimal Control of an ISS-Based Robotic Manipulator with Path Constraints
(S. Breun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
Rigorous Analysis of Extremely Large Spherical Reflector Antennas: Electromagnetic Case. (E.D. Vinogradova) . . . . . . . . . . . . . . . . . . . 177
Robust control of flexible manufacturing systems (J. Starke) . . . . . . . . . 178
Contributed presentations (theme: Chemical technology) . . . . . . . . . . 178 H 4
Absorbing Markov Chain in Gravitational Cascade Separation of Pourable
Materials at Different Stages of a Classifier (E. Barsky) . . . . . . . . . . 179
Modeling the Shelf Life of Packaged Olive Oil Stored at Various Conditions
(A. Kanavouras) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Analytical and Numerical Modelling of Multi-Channel Interactions in a Catalytic Reformer (A. Selsil) . . . . . . . . . . . . . . . . . . . . . . . . . 179
Thermal radiation influence on thermal explosion in a gas containing fuel
droplets. Quasi-steady balance case. (D. Katz) . . . . . . . . . . . . . . . 180
Factorial designs for variable selection in PLS to diagnose a batch chemical
process (M. Zarzo) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Robust Soft Sensors Based on an Ensemble of Symbolic Regression-Based
Predictors (E.M. Jordaan) . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Mathematical Modelling of Transport Equations in Fixed-Bed Adsorbers (A.
Perez Foguet) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Contributed presentations (theme: Materials) . . . . . . . . . . . . . . . . . 183 H 12
Identification of piezoelectric material parameters (B.K. Kaltenbacher) . . . 183
Representation of moving tools in 3D simulation models for industrial glass
forming processes (D. Hegen) . . . . . . . . . . . . . . . . . . . . . . . . 184
Fibre Motion in Turbulent Flows (N. Marheineke) . . . . . . . . . . . . . . 185
Numerical simulation of cylindrical induction heating furnaces (P. Salgado
Rodriguez) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
Theoretical molecular weight - rheology maps for linear polymers based on
the double reptation concept (C.F.J. den Doelder) . . . . . . . . . . . . . 186
Determination of Local Material Properties from the Shape of a Surface after
Microindentation (V. Bratov) . . . . . . . . . . . . . . . . . . . . . . . . 187
Contributed presentations (theme: Financial mathematics) . . . . . . . . . 187 H 14
Optimal Limit Order Strategies. (F.J. Gonzalez Padilla) . . . . . . . . . . . 187
Stochastic Volatility Models of Mean-Reverting Type Based on CARMA
Processes (N. Surulescu) . . . . . . . . . . . . . . . . . . . . . . . . . . 188
Rank Reduction of Correlation Matrices by Majorization (R. Pietersz) . . . . 188
Semi-Lagrangian Time Integration for PDE Models of Asian Options (S. Rout)189
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Pricing options with discrete dividends by high order finite differences and
grid stretching in space and time (C.W. Oosterlee) . . . . . . . . . . . . . 189
Mathematical modelling of industrial flow processes with complex
boundaries
J. Hunt (University College London)
Thursday, 13:30–14:30, Blauwe Zaal
In many industrial flow processes the boundaries of the flow region are so
geometrically complex that their effects on the flow cannot be computed in
detail. This lecture reviews the different approaches to improving and speeding up the approximation modelling of these effects. Where viscous high
Reynolds number flow passes between rigid obstacles (as in heat exchangers
or forest canopies) the optimum approximation depends on the length scale
and location over which the flow process has to be computed, for example
representing the local flows around densely packed obstacles in terms of simple dipole fields is shown to be sufficiently accurate for mean velocity and
dispersion calculations, but resistive continuum models are appropriate for
the average effects within and above a canopy (except around finite sized obstacles near its upwind/downwind boundaries). For these flows and inviscid
bubble flows, a critical feature is to deduce what definitions of average velocity (e.g. ‘interstitial’) are to be used for Eulerian or Lagrangian analyses of
flow processes.
An even more complex boundary is the randomly fluctuating at the outer
edge of turbulent flows where there are well defined discontinuities in velocity
and scalar quantities at the outer edge of turbulent flows. With these zones
now having been well established experimentally and computationally, it is
necessary to analyse their local flow fields in a randomly moving coordinate
system relative to this interface, i.e. taking a Lagrangian approach to the
classical Reynolds decomposition of the velocity into its mean and fluctuating
components. Some remarkably simple results emerge that are consistent with
much industrial practice. These seem to support Prandtl’s usually discredited
hypothesis that effectively the eddy viscosity (in fixed coordinates) is finite at
the edge of a turbulent shear layer!
Minisymposium: Electronic transport in semiconductor devices
L.L. Bonilla (Universidad Carlos III de Madrid)
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Miniaturization of electronic devices has reached the realm in which quantum
effects and fluctuations are very important. In this minisymposium modeling
and simulation of these phenomena are examined for different semiconductor
devices.
A deterministic multicell solution to the coupled Boltzmann-Poisson system simulating the transients of a 2D silicon MESFET
C. Ertler (Graz University of Technology), O. Muscato (Universita di Catania), F. Schürrer (Graz University of Technology)
The simulation of modern, nano-scaled semiconductor devices requires a detailed kinetic description of the occurring transport processes. Based on semiclassical grounds, this is achieved by the Boltzmann transport equation (BTE)
coupled with the Poisson equation. Finding a solution to the BTE is a difficult task owing to its complicated integro-differential structure. Indeed, the
stochastic Monte Carlo (MC) technique is widely used. State of the art applications of this method are able to simulate the carrier transport in complicated
device geometries by including realistic phonon dispersion relations and the
complete band structure of the considered semiconductor. However, in addition to the disadvantage of statistically noisy results, MC calculations are
frequently accompanied with great computational burden. Hence, alternative,
accelerated solution methods are most welcome. We present a new deterministic multicell method for solving the coupled Boltzmann-Poisson system for
spatially two-dimensional problems. The method is based on a discontinuous piecewise polynomial approximation of the carrier distribution function.
In this paper, the distribution function is assumed to be constant within tiny
cells of the phase space. We consider a non-parabolic six-valley model of the
conduction band of silicon. The multicell method is applied to simulate in
particular the transients of a two-dimensional silicon MESFET. The results
are compared with MC simulations.
Stochastic kinetic and drift-diffusion equations describing shot noise in
miniband semiconductor superlattices
G. Dell’Acqua (Universidad Carlos III de Madrid), L.L. Bonilla (Universidad Carlos III de Madrid), R. Escobedo (Universidad Carlos III de
Madrid)
We propose to model the effects of shot noise in semiconductor superlattices
by means of a Boltzmann-Langevin equation with a BGK collision term. In
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the hyperbolic limit of large electric fields, we derive from the kinetic equation a stochastic drift-diffusion equation by means of a consistent ChapmanEnskog method.
We present results of numerical simulations of the stochastic drift-diffusion
model and compare them with the corresponding deterministic equation. The
effects of shot noise are more noticeably near the threshold voltage for selfoscillations of the current through the device. It turns out that the shot noise
triggers the oscillations for voltages under threshold and enhance greatly the
variance of fluctuations near the threshold voltage.
Quantum kinetic and drift-diffusion equations for semiconductor superlattices
L.L. Bonilla (Universidad Carlos III de Madrid), R. Escobedo (Universidad
Carlos III de Madrid)
Quantum vertical transport in strongly coupled semiconductor superlattices
can be modelled by a Wigner-Poisson equation involving one miniband in
the simplest case. By using a consistent Chapman-Enskog procedure, we
derive a nonlocal (quantum) drift-diffusion equation for the electric field and
the electron density, provided the field contribution is of the same order as the
collision terms in the kinetic equation.
We present numerical solutions of the resulting problem for a device consisting of a n-doped superlattice placed in a n+-n-n+ diode and subject to a
constant voltage bias. For large enough voltage self-oscillations of the current through the superlattice result. We discuss the differences between these
results and those obtained by using a semiclassical approximation.
Hydrodynamic transport models for an ultra-thin base Si Bipolar Transistor.
M. Muscato (Universitá di Catania)
Hydrodynamic models for carrier transport in semiconductors can be derived
by taking moments of the Boltzmann Transport Equation. The Maximum Entropy Principle allows us to obtain a closed hydrodynamic model, containing
no free parameters, in order to describe transport phenomena under conditions very far from thermodynamic equilibrium.
Under suitable scaling assumptions, the above model reduces to the Energy
Transport model, to the Navier-Stokes-Fourier model, or to the Drift Diffusion one , in which all the transport coefficients are now explicitly determined.
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In this paper we study the applicability of these models, to an ultra-thin
base npn silicon bipolar transistor where the transport is quasi ballistic. The
validity of the constitutive equations for the fluxes and the production terms
(which are the moments over the collisional operator) is investigated by using
Monte Carlo simulations.
Domain Displacements and Ramping Time in Superlattices
B. Birnir (University of California, Santa Barbara), O. Romero (Univ. de
Granada), J. Soler (Univ. de Granada)
The relationship between the displacement of domain boundaries and ramping time in biased superlattices is explored using the avoided crossings (anticrossings) in the spectrum of mesoscopic superlattice states. It is shown that
the allocation of the domain boundaries can be explained in terms of LandauZener computation of the probability of the event, that states of an initial
domain jump avoided crossings of the states of the final domain. The theory
predicts numerical simulations, this agreement is exhibited and the numerical
methods explained.
Minisymposium: Robust numerical methods for singularly perturbed
multiscale flow problems II
The study of many theoretical and applied flow problems in science and technology leads to boundary value problems of singularly perturbed partial differential equations that have a multiscale character. Thus, it is of considerable
scientific interest to develop a solid mathematical theory and specific computational methods for singularly perturbed multiscale problems and related
problems arising from applications. The design of robust numerical methods
for such problems, i.e. methods whose accuracy does not depend on local
scales of singular components of the solution, is an important task. The symposia I and II will discuss numerical methods for convection diffusion equations, related iterative solution methods and also numerical methods for more
complex flow problems. Invited speakers refer to each others approaches.
The contributions are in part supported by N.W.O. grant 047.016.008.
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On Massively Parallel Finite Element Methods for Convection-Diffusion
Problems
Massively parallel iterative algorithms for convection-diffusion equations
where introduced in W. Layton, J. Maubach, P. Rabier, Num. Math. 71
(1995), 29 – 58. For convection-diffusion equations discretized with the Finite Element Method on computational grids with local bisection refinement
presented in J. Maubach, SIAM J. Sci. Comput. 16 (1995), 210 – 227], the
speedup of the iterative methods is examined. Excellent speedup is obtained
due to a simple and efficient spacefilling curve technique particular to the
used grid refinement. Examined will be the performance of the standard nonconforming basis functions as well as the degree 3 variant in [J. Maubach, P.
Rabier, submitted].
Local defect correction with compact finite difference schemes for convectiondiffusion equations
M. Sizov (Technische Universiteit Eindhoven)
We study the possibility of combining of the Local Defect Correction (LDC)
with high order compact finite difference schemes for flow problems. As
a model equation for such study we choose stationary convection-diffusion
equation. Local Defect Correction technique was first developed for pure
diffusion problems and therefore we need testing of it in application to convection dominated and pure convection problems. First we investigate the
convergence behaviour of LDC technique in combination with central difference and/or upwind schemes. We are able to theoretically estimate the convergence factor for such combination. Numerical simulations are in a good
agreement with theoretical estimations. The next step is to study the possibility of combination the LDC technique with high order compact schemes. An
algorithm was developed first for 1D stationary convection-diffusion equation, which was extended later to 2D problems and could be generalized for
3D problems. The results of testing shows that we get the same accuracy of
the solution as on the reference uniform grid with much less points in the
domain.
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A Fully Conservative Model for Compressible Two-Fluid Flow
J. Wackers (CWI, Amsterdam), B. Koren (CWI)
Most interface-capturing methods for compressible two-fluid flows combine
the single-fluid flow equations with one extra equation. This equation distinguishes between the fluids by defining a mixed-fluid parameter, used in the
equation of state. It has been shown that conservative formulations of such
equations often produce large pressure errors. This problem can be solved by
using locally non-conservative methods, but for flows with strong shocks and
large density jumps, a fully conservative method is preferred. In that case, the
full two-phase flow equations are usually solved.
Here, an intermediate approach is presented: a conservative formulation
which is simpler than two-phase, because it has one pressure and velocity for
the fluids. The single-fluid conservation laws are combined with two extra
equations: conservation of mass and energy for one of the fluids. The last
equation contains a source term, to account for the energy exchange between
the two fluids. No mixed-fluid quantities are needed whatsoever.
Explicit expressions are found for this source term in contact discontinuities and shocks. For the discretisation of the flow equations, a HLL Riemann
solver is adapted for two-fluid flow. This solver gives good results without
needing characteristic speeds, which are hard to obtain in mixed fluids. Furthermore, it allows an elegant treatment of the source term. The result is a
solver for gas-gas and liquid-gas flows, suitable for problems with high density ratios. Results will be shown, e.g., for test problems with strong shocks
hitting two-fluid interfaces.
Two-Phase Simulations of Water Waves in the Offshore Industry
R. Luppes (University of Groningen), A.E.P. Veldman (University of
Groningen)
Two-phase (or even multi-phase) flows frequently occur in a wide range of
industrial applications as well as in many situations in the shipping and offshore industry. The impact loading of large water waves on floating objects
(ships, platforms) is an important subject of study, as this may result in serious damage. By carrying out flow simulations, the behavior of water waves
can be studied, which enhances the knowledge and understanding of the phenomenon of wave impact loading.
In many studies of two-phase flows, only one phase (water) is simulated
and the second phase (air) is neglected. In this one-phase approach, the effect
of the second phase on the first is modeled by extrapolation of the pressure at
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the free surface. The water velocities are a consequence of the extrapolated
values of the pressure. In fact, boundary conditions at the free surface, in
terms of velocity, pressure and curvature of the free surface, describe the
interaction between the two phases.
In the two-phase approach, both phases are simulated. No boundary conditions have to be applied at the free surface, which means that the pressure
and velocities at and near the free surface are naturally obtained in the solution. This results in a better description of the free surface and hence of the
water waves, when compared with measurements. The discontinuity of the
fluid properties (density, viscosity) across the free surface requires a carefully
designed interpolation scheme of these properties. If properly chosen, this
results in a further improvement of the description of the free surface.
The methods described above are demonstrated with applications in the
offshore industry. However, they can be applied in other (industrial) cases of
two-phase flows as well.
Analysis of a multigrid method for convection-diffusion problems
M.A. Olshanskii (Moscow M.V. Lomonosov University)
In the talk we present a convergence analysis of a multigrid solver for a
system of linear algebraic equations resulting from the disretization of a
convection-diffusion problem using a finite element method. We consider
piecewise linear finite elements in combination with a streamline diffusion
stabilization. We analyze a multigrid method that is based on canonical intergrid transfer operators, a ‘direct discretization’ approach for the coarse-grid
operators and a block type smoother. A robust (diffusion and h-independent)
bound for the contraction number of the two-grid method and the multigrid W-cycle are proved for a special class of convection-diffusion problems,
namely with Dirichlet (and also mixed Dirichlet-Neumann) boundary conditions and a flow direction that is constant and aligned with gridlines. Our convergence analysis is based on modified smoothing and approximation properties. The arithmetic complexity of one multigrid iteration is optimal up to a
logarithmic term. More details of the analysis can be found in [1, 2].
[1] Olshanskii, M.A. and Reusken, A.: Convergence analysis of a multigrid method
for a convection-dominated model problem, to appear in SIAM J. Numer. Anal.
[2] Olshanskii, M.A.: Analysis of a multigrid method for convection-diffusion equation with the Dirichlet boundary conditions, to appear in J. Comp. Math. and
Math. Phys.
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Minisymposium: Combustion Simulation
In this minisymposium we present some numerical methods relevant to the
simulation of gaseous combustion. These simulations are generally very difficult, since they require the simultaneous solution of the flow equations and
(the many) combustion equations. Moreover, these equations are extremely
nonlinear and stiff. This puts high requirements on numerical methods and
computer resources. A lot of research is directed towards reducing the computational costs of combustion simulation, either by improving numerical
methods, applying reduction techniques or better turbulence modelling. The
subjects covered are: discretisation methods, gridding methods, reduction
techniques and turbulence modelling.
The first talk addresses the topic of space discretisation. More in particular,
a modified exponential scheme is presented, that is uniformly second order
accurate, even for convection dominated flows, and that reduces numerical
diffusion significantly.
In the second talk, the speaker will talk about the local defect correction
(LDC) technique applied to laminar flames. LDC is a two-grid method, employing a global coarse grid and a local fine grid, needed to capture the detailed structure of laminar flames. The new feature in this presentation is to
use a curvilinear local grid that thightly fits the flame front.
The third talk is devoted to reduction techniques, i.e. methods to reduce the
number of species significantly, without too much loss of accuracy. In particular, the phase space ILDM method is introduced, with is a generalisation of
the classical ILDM method, in that it takes into account not only the chemical
reactions, but also diffusion.
The last talk concerns turbulent flames and deals with regularisation methods for the flow and combustion equations. The Leray and NS-alpha approaches are extended to include the combustion equations. The accuracy of
the regularization approach will be assessed through comparison with direct
numerical simulations of turbulent flames.
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An exponential scheme for the numerical simulation of laminar flames
In this talk we discuss an exponential scheme for the discretisation of the
convection-diffusion-reaction equation, which is a model problem in laminar flame simulation. More specifically, we introduce an exponential scheme
for the computation of the numerical fluxes. The numerical fluxes at the cell
edges are computed from the corresponding PDE, including the source term.
This way, we obtain a second order accurate scheme, uniformly in the Peclet
number. Moreover, cross-wind diffusion in 2D computations is reduced significantly. We will apply this scheme to 1D flames with complex chemistry
and 2D flames with one-step chemistry.
Local Defect Correction for Laminar Flame Simulation
M. Graziadei (Technische Universiteit Eindhoven)
Boundary value problems with high activity regions are efficiently solved by
the LDC method: an iterative method that uses a global coarse and a local fine
structured grid, providing the way to exchange information between them.
If applied to curvilinear orthogonal fine grids that tightly follow the shape
of the solution, it gives rise to an algorithm that reduces significantly the
computational complexity. We have successfully applied this method to the
thermo-diffusive model for laminar flames.
The Phase-Space Intrinsic Low-Dimesional Manifold method to reduce
chemical kinetics
H. Bongers (Technische Universiteit Eindhoven), L.P.H. de Goey (Technische Universiteit Eindhoven)
In spite of the increasing amount of computer power, accurate simulation of
combustion systems is still restricted to relatively simple configurations. To
be able to model more complex burner systems, the use of chemical reduction techniques is inevitable. In general, the reduction is achieved by applying
steady-state assumptions for fast processes. In the past decades, a number of
reduction methods has been introduced. Among these methods, the Intrinsic
Low-Dimensional Manifold (ILDM) method has proven to be a successful
method. However, one of the drawbacks of ILDM is that diffusion is not
taken into account during the construction of the reduced mechanism. The
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Flamelet-Generated Manifold method is a reduction method in which diffusion is taken into account, leading to more accurate predictions of, for instance, the burning velocity of premixed flames. One of the disadvantages
of the FGM method is that it is less mathematically sound than ILDM. The
recently introduced method Phase-Space ILDM (PS-ILDM) uses the mathematical algorithm of ILDM applied on the equations of FGM, which results in
a mathematical sound reduction method, which includes diffusive processes.
The derivation of the PS-ILDM algorithm discussed. In addition, some practical examples of the reduction method will be presented.
Regularization modeling of turbulent flames
B.J. Geurts (University of Twente)
The accurate simulation of all dynamically relevant properties of turbulent
flames requires extensive computational effort. Instead, spatially filtered turbulent flame formulations can be developed which are suitable for capturing
the primary flame features at strongly reduced costs. In order to arrive at an
accurate large-eddy approach to turbulent combustion, a proper representation of the turbulent fluid flow is essential. For this purpose direct regularization of the quadratic nonlinearity in the Navier-Stokes equations will be studied, of which the Leray and NS-alpha approach are important examples. An
extension of this direct regularization to include the treatment of the reacting
species will be presented. The accuracy of the regularization approach will be
assessed through comparison with fully resolved direct numerical simulations
of decaying homogeneous turbulence in combination with simple combustion
modeling. The flame structuring and interaction with the turbulent flow will
be quantified in terms of global geometric properties of evolving flame surfaces and attention will be paid to surface-area and flame wrinkling. Both
passively transported flames as well as flames which directly couple to the
fluid flow equations will be considered.
Contributed presentations (theme: Aerospace)
Mathematical Modeling of Plasma and Sheath
N. Sternberg (Clark University)
A model for the collisionless plasma-wall problem under the action of a magnetic field is developed, and the behavior of the plasma characteristics is discussed. The plasma and the sheath are then modeled separately to obtain the
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position of the quasi-neutral plasma boundary and of the sheath edge. Studying the behavior near the plasma boundary and the sheath edge, the plasma
and the sheath solutions are patched together to approximate the solution of
the plasma-wall problem.
Unsteady Heat Load Reduction at the Reentry of a Future Mars Express
Capsule
R. Callies (Technische Universität München)
Flight time is an important limitation for future Mars exploration. Express trajectories from Earth to Mars are possible, if higher rendezvous velocities are
accepted. Due to fuel limitations the additional speed has to be annihilated by
aeroassisted braking in the Martian atmosphere. Speed is converted to heat,
which is added to the anyway high thermal load of a normal reentry procedure. Sophisticated thermal protection systems are required to withstand the
high temperature without increasing the mass of the thermal shield. The purpose of those systems basically is to avoid inadmissible high temperatures in
the inner parts of the vehicle.
In the paper, the three-dimensional Mars reentry problem is addressed from
the point of view of extended flight control; it is shown that trajectory optimization is an efficient means to reduce the heat input into the vehicle. A
realistic mathematical model has been developed which takes account of the
unsteadiness of the heat flux through the thermal protection system of a future Mars Express capsule. The parabolic heat equation is coupled to the
nonlinear ODEs resulting from the equations of motion of the reentry vehicle. Coupling is done via an adaptive discretization of the PDE and the
treatment of the time evolution by the method of lines. Numerical difficulties
arise from the difference between the fast dynamics of the capsule and the
slower dynamics of the temperature process. The coupled system forms the
core of a minimax optimal control problem minimizing interior temperature.
Additional heat and dynamic pressure constraints lead to state constraints of
first and second order. After proper transformations the complete problem
of optimal control is transferred into a multi-point boundary value problem.
The numerical solution of the boundary-value problem is obtained with high
accuracy by the advanced multiple shooting method JANUS for DAEs.
Optimal Control of an ISS-Based Robotic Manipulator with Path Constraints
S. Breun (Technische Universität München), R. Callies (Technische Universitaet Muenchen)
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To reduce time-consuming extravehicular activities onboard of the International Space Station ISS, a promising approach is to substitute robotic manipulators for missing manpower. Important steps to maintain operational safety
are monorails attached to the ISS structure and partly guiding the robot’s
motion, the spatial prescription of the end-effector trajectories and a motion
planning that takes into account the reduced accuracy of the linear motion
compared to the rotational joints.
We investigate optimal path-constrained trajectories of a three-link robot
with the monorail as additional fourth and prismatic joint. Operation of the
highly accurate end-effector makes sense only after the low accuracy monorail motion stopped. This leads to a problem of optimal control for a nonlinear system of differential-algebraic equations under multiple restrictions
and with several interior points. Objective functions are minimum-time motions and motions with minimum force impact on the ISS. The algebraic constraints are eliminated by transformations into minimum coordinates. The
only remaining control is the acceleration of the end-effector along the given
trajectory, replacing four actuator torques/forces. The price to be paid for a
simpler structure are piecewise defined equations of motion, two highly nonlinear control constraints and two state constraints of first order. Switching
points between partly linear and fully rotational motion are optimized simultaneously. The problem of optimal control theory is transformed into a multipoint boundary value problem. The differential equations for the state and adjoint variables are recursively defined to allow efficient treatment; prismatic
and rotational joints are handled in a unified manner. The numerical solution
of the boundary value problem is by the advanced multiple shooting method
JANUS. Solutions are presented including touch points of the state constraints
with both control constraints being active simultaneously; this leads to a new
type of interior point conditions.
Rigorous Analysis of Extremely Large Spherical Reflector Antennas:
Electromagnetic Case.
E.D. Vinogradova (Macquarie University), S.S. Vinogradov (University
of Sydney), P.D. Smith (Macquarie University)
Recently we analysed acoustically hard (or soft) extremely large Spherical Reflector Antennas (SRA). The success for extremely large wavelength
structures was due to a uniquely efficient solution of the second kind matrix
equation derived with the Method of Regularisation (MoR) for the associated
boundary value problem. The key was the use of the fast Fourier transform
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(FFT) to reduce dramatically the computational cost of the conjugate gradient
algorithm (BI-CGSTAB) for solving the matrix system. These mathematical
tools provided accurate solutions of a hard SRA with aperture size from 100
to 5000 wavelengths. In this paper we extend these ideas to the electromagnetic case and examine the SRA with a metallic dish and feed that generates
a beam-like distribution across the aperture. The same rigorous approach
(MoR) reduces the problem to a coupled linear system of second kind. The
FFT/BI-CGSTAB approach employed in the acoustic case must be significantly modified. As the electrical size of the SRA increases, the imbalance
between the two sets of ‘electrical’ and ‘magnetic’ Fourier coeffients (in the
norm sense) grows so much that the direct application of BI-CGSTAB to the
coupled system becomes very much less efficient than that for the acoustic
SRA. Two approaches overcome this difficulty. First, the initial equations are
rearranged so that the two coefficient sets are more balanced. This rearrangement allows us to study aperture sizes up to 300 wavelengths. Secondly, when
the aperture size exceeds 200 wavelengths, we employ some remarkable features of the initial equations to replace them by their asymptotic versions.
These versions are ideally suitable for BI-CGSTAB and extend the limit of
effective computation for aperture sizes up to 2000 or more. The numerical
calculations are presented.
Robust control of flexible manufacturing systems
J. Starke (University of Heidelberg), C. Ellsasser (University of Heidelberg)
Time-dependent robot-target assignment problems with several autonomous
robots and several targets are considered as model of flexible manufacturing
systems. Each manufacturing target has to be served in a given time interval
by one and only one robot and the total working costs have to be minimized
(or total winnings maximized). A specifically constructed dynamical system
approach (coupled selection equations) is used which guarantees feasiblitiy
of the assignment solutions. This type of control is based on pattern formation principles (known in physics, chemistry and biology) and results in fault
resistant and robust behaviour. The performance of the suggested control
is demonstrated and visualized with a computer simulation of autonomous
space robots building a space station by distributed transporting several parts
from a space shuttle to defined positions at the space station.
Contributed presentations (theme: Chemical technology)
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Absorbing Markov Chain in Gravitational Cascade Separation of Pourable
Materials at Different Stages of a Classifier
E. Barsky (Negev Academic College of Engineering)
We consider the gravitational cascade separation process as an absorbing
Markov Chain. We will receive a new method for calculating a degree of
fractional extraction for any narrow class of pourable material in cascade classifier at different stages and a few other intresting results.
Modeling the Shelf Life of Packaged Olive Oil Stored at Various Conditions
A. Kanavouras (Unilever BestFoods, Europe), F.A. Coutelieris (UnileverBestfoods R and D Centre), A.K. Kanavouras (Unilever BestFoods,
Europe)
A model was applied to experimental data to study the mass transport of oxygen diffusing through the oil phase and the packaging materials as well as the
oxidation reactions. The nonlinear system was numerically solved for various
combinations of materials, temperatures, and light availability, by adopting a
typical Newton method, in conjunction with a multi-step up-winding finite
differences scheme. The possibility of the packaged olive oil not to reach the
end of its shelf life (Psafe) and its time evolution, was in very good agreement with the experimental data. Psafe was proposed as a reduction indicator
for shelf life predictions at “real-life” conditions. Exposure to light at any
pattern could significantly stimulate the oxidative degradations, only assisted
by elevated temperatures and presence of oxygen. Plastic containers showed
particularly higher protective role when oil was stored at light, while glass
was the most protective material when oil was stored at dark.
Analytical and Numerical Modelling of Multi-Channel Interactions in a
Catalytic Reformer
A. Selsil (University of Liverpool), A.B. Movchan (University of Liverpool), N.V. Movchan (University of Liverpool)
The aim of this work is to develop a new design for an efficient and environmentally friendly catalytic reformer, used to produce hydrogen for fuel cells.
This new device consists of a large number of parallel channels, separated by
thin walls, with exothermic and endothermic reactions occurring in adjacent
channels. The industrial novelty of this design is that the two reactions are
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coupled by the heat transfer process across the connecting wall, and are operated in parallel, rather than in series. The mathematical model involves a
system of reaction-diffusion equations coupled with algebraic equations. We
use asymptotic analysis to analyse the heat transfer across the thin-walled
structure by exploiting the fact that the ratio of the width of the wall to the
width of the channel is sufficiently small. We first investigate the temperature
and concentration distributions involved in linear steady-state heterogeneous
equations for reactions occurring in packed bed catalytic reformers. We analyse the case when the wall consists of layers of different widths and thermal
conductivities (for details see [1]) including heat transfer via radiation for a
wall with an air gap. We then obtain a full analytical solution using a compound asymptotic technique for this linear model and analyse the boundary
layer solutions in detail. We extend the problem to the nonlinear case where
we use matched asymptotic expansions to find the analytical solution. Graphical results are presented showing the accuracy of the solution; the boundary
layers are given explicitly to show how the temperatures behave in small regions close to the ends of the channels. Further work includes introducing
transient terms and analysing stability of solutions.
[1] Selsil, A., Movchan, N.V., Movchan, A.B., Kolaczkowski, S.T., Awdry, S.,
Mathematical Modelling of Heat Transfer in a Catalytic Reformer - to appear
in IMA J. Appl. Maths. (2004)
Thermal radiation influence on thermal explosion in a gas containing fuel
droplets. Quasi-steady balance case.
D. Katz (Ben Gurion University of the Negev), V. Gol’dshtein (Ben Gurion University of the Negev), I. Goldfarb (Ben Gurion University of
the Negev)
A study of the delayed regimes of droplet ignition phenomena is presented.
Spray ignition is considered as an explosion problem. Physical processes
incorporated in the model are evaporation, heat transfer and highly exothermic oxidation reaction. The analysis is spatially homogeneous and adiabatic.
Changes of the pressure and gas mixture density are not accounted for. Combustible gas component is deficient. Thermal conductivity of the liquid is
much higher than that of the gas. Heat transfer coefficient depends only on the
gas thermal properties. Spray is monodispersive. A first-order highly exothermic reaction represents appropriate chemical reaction. Additional connection
comes from the Clausius-Clapeyron law. Droplets are regarded as a source of
the endothermicity. The set of governing equations represents a multi-scale,
conventional, singularly perturbed system of ODEs. Geometric version of the
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method of integral manifolds allowing decomposition of the phase space analysis into separate studies of its fast and slow subsystems is used [1]. For the
fast gas temperature the delay time increases with increasing droplets number
and the ratio between the intensities of the combustion and evaporation processes. It decreases with the increasing dimensionless droplet radius and the
ratio of radiative and convective heat transfer coefficients. Radiative heat flow
increases the delay time. For the fast droplet radius the delay time decreases
with the increasing droplets number and the ratio between the intensities of
the combustion and evaporation processes. It increases with the increasing
droplet radius and the ratio of radiative and convective heat transfer coefficients. Radiative heat flow decreases the delay time.
[1] Gol’dshtein V.M. and Sobolev V.A. 1992 Singularity Theory and Some Problems of Functional Analysis (AMS Translations, series 2, vol. 153)(Providence,
RI:American Mathematical Society) pp 73-92.
Factorial designs for variable selection in PLS to diagnose a batch chemical process
M. Zarzo (Polytechnic University of Valencia), A. Ferrer (Polytechnic
University of Valencia)
Batch chemical processes are difficult to control due to the complex nonlinear reaction kinetics that take place. In a batch chemical process studied (the
elaboration of a polymer), the evolution versus time (trajectory) of 50 process
variables (pressures, temperatures, ...) are available for a set of 69 batches,
elaborated in two different periods. At the end of the process, one quality
parameter is analysed (the hydroxyl number), that presents an excessive variability from batch to batch. To diagnose the causes, a PLS regression has
been conducted with the 8500 variables that comprise the trajectories available from every batch. Although the first component is statistically significant, the diagnosis of the process is not easy. A new approach is presented
with this objective, selecting the blocks of variables (trajectories) that present
in the PLS model a significant effect in the goodness of prediction obtained by
cross-validation (Q2). This procedure uses fractional factorial designs with
factors at two levels, and analyses what effect produces in the Q2 the fact
that a trajectory is included or not in the model. Also another factor (period
of the batch) has been introduced to study the consistency of the PLS model
between the two periods of batches studied.
Analysing the results, only the trajectories from two of the four stages of
the process have a significant effect in the goodness of prediction. Carrying
out a new fractional factorial design with the trajectories of these stages, it
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results that only one of them has a clearly significant effect in the Q2, but it
depends on the set of batches included in the model. This analysis reveals
that the causes of variability of the hydroxyl number are not exactly the same
in all batches, and highlights the stages and trajectories that require a further
study.
Robust Soft Sensors Based on an Ensemble of Symbolic RegressionBased Predictors
E.M. Jordaan (The Dow Chemical Company), A.K. Kordon (The Dow
Chemical Company), H. Chiang (The Dow Chemical Company)
Soft sensors or inferential sensors are mathematical models used to predict the
quality variables of processes. The need for robustness toward process variability, the ability to handle industrial data (e.g., missing data, measurement
noise, operator intervention on data, etc.) and ease of model maintenance are
key issues for mass-scale application of reliable inferential sensors. However,
the capabilities of the neural networks, which are the dominant approach in
the existing industrial soft sensors, are limited. One way to increase the robustness is to use explicit nonlinear functions that are derived automatically
by symbolic regression, generated by genetic programming. A major advantage of this approach is that there is a potential physical interpretation of the
model. These non-black box models are more acceptable for process engineers. Other advantages are the ability to examine the extrapolation behavior
of the model and to impose external constraints on the modeling process.
However, one of the key improvements from an industrial point of view is to
use ensembles of symbolic regression-based predictors. There are a number
of advantages to ensembles of predictors instead of a single model. Firstly,
since the prediction is a weighted average of a number of predictions, one
obtains a more consistent estimate of the output. Secondly, the spread or
variance of the different predictions can be used to derive a measure of confidence. A third advantage is that this measure of model disagreement can
be used for problem detection. Another advantage of the ensemble is that
the soft sensor can be made robust toward the failure of equipment measuring the input variable by choosing models with different input parameters. In
this paper we will also demonstrate a number of successful industrial applications of robust soft sensor by using ensembles of symbolic regression-based
predictors in continuous and batch processes.
Mathematical Modelling of Transport Equations in Fixed-Bed Adsorbers
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A. Perez Foguet (Universitat Politécnica de Catalunya), A. Huerta Cerezuela
(Universitat PolitFcnica de Catalunya)
In this work, the transport equations in fixed-bed absorbers are presented and
analyzed. Special attention is dedicated to model nonlinear adsorption and
desorption processes that typically take place at particle level [1, 2]. The
presentation starts from the general mass and energy balance equations. After that, some general hypotheses are summarized and the work focuses in
the analysis of isothermal and incompressible problems. In these cases the
governing equations are reduced to a convection-diffusion-reaction equation
coupled with the intraparticle transportation ones.
A dimensionless analysis allows particularizing the mathematical model
into four different cases depending on the relative importance of the physical
phenomena involved. Then, a detailed analysis of the so-called ‘loading’
problem is carried out. This problem is characterized by an input flow with
higher concentration than the one initially present in the absorber. It is wellknown that in this situation vertical fronts are formed in the solution if nonlinear equilibrium relationships are considered. In this context, this work
shows how the choice of the main variable of the problem is critical in order to
verify the general principle of mass conservation. The presentation finalizes
with some examples related with the automotive industry, emphasizing the
main difficulties found in the numerical resolution of them.
[1] P.C.Wankat, Rate Controlled Separations. Blackie Academic and Professional,
Glasgow, (1994).
[2] M.A.Hossain, D.R.Yonge, Finite Element Modeling of Single Solute Activated
Carbon Adsorption, Journal of Environmental Engineering (1992), 118 (2), 238252.
Contributed presentations (theme: Materials)
Identification of piezoelectric material parameters
B.K. Kaltenbacher (University of Erlangen)
Piezoelectric transducers that transform mechanical into electric energy and
vice versa, play an important role in many technical applications ranging from
ultrasound generation in medical imaging and therapy to injection valves in
common rail diesel engines. For the development of piezoelectric sensors
and actuators by means of numerical simulation, precise knowledge of the
elastic stiffness coefficients, the dielectric coefficients and the piezoelectric
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coupling coefficients is necessary. The topic of this talk is identification of
these material parameters from voltage-current measurements. Especially,
we focus on the nonlinear situation, where due to large excitations, some of
the material parameters are not constants any more but depend on the electric field strength. Determining this functional dependence from the given
measurements, amounts to a parameter identification problem for a system of
nonlinear partial differential equations. This is numerically solved by a Newton type scheme, where the inherent ill-posedness of the inverse problem is
accounted for by restricting the number of degrees of freedom, so by regularization by coarse discretization. Here, a formulation of the PDEs in frequency
space via a so-called multiharmonic ansatz turns out to be both natural with
respect to the measurements and efficient for the task of parameter identification. Reconstruction results from measured data are supposed to demonstrate
applicability the proposed methodology.
Representation of moving tools in 3D simulation models for industrial
glass forming processes
D. Hegen (TNO Glassgroup), G.A.A.V Haagh (TNO Glassgroup), O.M.G.C.
op den Camp (TNO Glassgroup)
Current industrial forming processes for glass products (such as TV-panels,
tableware and glass containers) have been used for decades and are generally
considered as mature. Yet, market demands urge glass manufacturers to continuously improve their process in order to reduce reject, increase production
speed and decrease product weight, and to be always flexible in order to fabricate new products. To extend process optimisation and innovation beyond
widely used empirical approaches, the application of 3D forming simulation
models is becoming more and more important. Several steps of typical glass
forming processes involve moving tools that influence the flow of hot glass
profoundly. For a good model of such process steps an accurate representation of the geometry of the process set-up is required at each stage. Although,
remeshing techniques and computer power have advanced the latest years,
models involving moving tools that apply remeshing still suffer from severe
drawbacks as the transfer of calculated properties from one finite element
mesh to another mesh may introduce inaccuracies and instabilities. Furthermore, 3D forming simulation models that apply remeshing are still too slow
for sensitivity analyses of process settings and product geometries. In the
3D glass forming simulation models of the TNO Glass Group, remeshing is
avoided. The applied approach is based on a fixed volume mesh and a tool
surface representation only. At each stage of the process elements that cover
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the tool surface are temporarily adapted for an accurate representation of the
tool. The advantages of the approach will be demonstrated by means of results for the process step of a glass delivery system where the glass flow is
dominated by a rotating and translating stirrer and for the process step where
a moving plunger presses (and cools) hot glass to an intermediate or final
product shape.
Fibre Motion in Turbulent Flows
N. Marheineke (Fraunhofer ITWM)
The understanding of turbulent flows is of great interest for research, development and production in the textiles manufacturing. In the melt-spinning
process of nonwoven materials, hundreds of individual fibres being obtained
by continuous extrusion of a melted polymer are stretched and entangled by
highly turbulent air flows to finally form a web. The quality of this web and
the resulting nonwoven material depends essentially on the dynamics of the
fibres. Fibre-turbulence is hereby a complex phenomenon that is governed
by many factors, including nature of flow field, length scales of turbulence,
concentration and size of fibres. Thin fibres decrease the turbulent intensity,
probably by increasing the apparent viscosity, whereas thicker fibres - greater
than some critical particle Reynolds number - increase the intensity, perhaps
due to vortex shedding. Both mechanisms are strongly affected by the concentration. Assuming no significant affection of the turbulence by the fibres,
the structure of the turbulent flow is analysed without consideration of suspended fibres. Based on the k-ε model and Kolmogorov’s energy spectrum a
Gaussian fluctuation velocity field is derived. This enables the modelling of
a corresponding stochastic force representing the turbulence effects on a long
slender elastic fibre. Asymptotic analysis of the fibre dynamics described by
a system of stochastic PDEs shows that the stochastic force term can be numerically treated as white noise with flow dependent amplitude. Simulations
yield very satisfying results in comparison to the experimental measurements
of the spinning process.
Numerical simulation of cylindrical induction heating furnaces
P. Salgado Rodriguez (Universidade de Santiago de Compostela), A.
Bermúdez (U. de Santiago de Compostela), D. Gómez (U. de Santiago
de Compostela)
The induction heating is widely used in an important number of industrial
applications related to metals processing operation. The induction heating
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process is very complex and involves different physical phenomena: electromagnetic, thermal with change of phase and hydrodynamic in the liquid
metal. Therefore, numerical simulation is an important tool to design induction heating systems and to know their behavior.
From a mathematical point of view, we must solve a coupled non-linear
system of partial differential equations which arises from a thermal-magnetohydrodynamic problem. All of the models are coupled because physical parameters depend on temperature, heat source in the thermal problem is Joule
effect, liquid domain of the hydrodynamic model depends on temperature
and velocity of liquid metal appears in the Ohm’s law. In the literature we
can find several publications devoted to numerical solution of some of the
problems cited before, but none of them deals with the coupling between the
three models.
In this work, we are going to introduce and numerically solve only the
thermoelectrical problem which arises in a cylindrical induction heating furnace. By assuming cylindrical symmetry, we describe the problem in a twodimensional domain and propose a finite element method for its numerical
solution. In order to take into account the change of phase, we write the heat
transfer equation in terms of the enthalpy and propose an iterative algorithm
to numerically solve the resulting non-linear problem. To handle the coupling
between the thermal and electromagnetic problem we propose a fixed point
algorithm.
We complete the work by giving a family of analytical solutions of the
thermoelectrical problem under simplified assumptions on geometry and data.
Finally, we present numerical results obtained with the two-dimensional code
for an industrial furnace used in silicon purification.
Theoretical molecular weight - rheology maps for linear polymers based
on the double reptation concept
C.F.J. den Doelder (Dow Benelux B.V.)
The connection between molecular structure and viscoelastic properties of
polymers is complex. Still, understanding this connection is critical for new
product development. The present paper explores two recent models to construct relations between various molecular weight averages and two of the
most important linear viscoelastic quantities. The models are DRSE (double reptation with a single exponential relaxation function) and TDD-DR
(time-dependent diffusion double reptation). The linear viscoelastic quantities considered are the zero-shear viscosity and the recoverable compliance.
The exploration is done via a theoretical design using three model distribution
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shapes: uniform, log-normal, and bimodal. The resulting maps illustrate the
effect of the shape of the distribution on the rheology. The maps can be useful
for designing new polymers for specific applications. It is recommended to
validate the model predictions with well-controlled experimental data.
Determination of Local Material Properties from the Shape of a Surface
after Microindentation
V. Bratov (Malmö Högskola)
A possibility to evaluate material properties (like, for example Young’s modulus, Poisson’s ratio and parameters of plasticity) in a definite point of a definite sample is of a great interest for many applications. One of the examples
is the need to study the changes in the mechanical parameters of biomaterial samples in a region adjacent to the border between two materials. Other
possible implementation can be a nondestructive study of the properties of
a unique sample (turbine blade, utilized construction etc.). An experimental
technique, being able to provide information about local mechanical properties of material in a vicinity of any point is required. Proposed solution to the
problem is based on a study of a profile of material surface, subjected to microindentation along with a Finite Element Method (FEM) simulation of the
indentation process. Using previously developed optical method to measure
the profile of a surface, imprints made by Future-Tech FM-1e microhardness
tester with Wickers and Rockwell-type indenters in steel and copper were
studied. Along with this the FEM modelling of the indentation process was
performed. Afterwards the inverse analysis of the measured surface profile is
executed, tending to optimise the mechanical properties of the material used
in FEM simulation, so the results of the latter coincide best with the measured
profile.
Contributed presentations (theme: Financial mathematics)
Optimal Limit Order Strategies.
F.J. Gonzalez Padilla (TPD-TNO), G. Iori (Deparment of Mathematics),
M. Zervos (Deparment of Mathematics)
A limit order is one of the basic tools for trading. Differently from market
orders that are immediately executed, limit orders allow to wait for a convenient price to buy or sell. Typically, the trader will be issuing an order to buy
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or sell at a pre-specified price. By delaying the transaction, limit order traders
hope to obtain a more favourable price, but face uncertainty over when the
transaction will be done and risk, if the order is not matched, not to trade at
all.
Traders can opt between different strategies, namely different execution
prices and different time span for the limit orders. The value of a given strategy is defined as the profit obtained by a limit order compared to the one obtained by using a market order. In this paper, we will focus on the existence
of optimal strategies. We will numerically analyse how different stochastic
models for the underlying asset affect the value of the strategy and the existence of an optimal value. We will also study the case in which buy and sell
prices differ (ask-bid spread). We will show that in fact there exist some optimal strategies. A different approach to optimality emerges when we consider
the risk. We will briefly discuss this subject.
PDE derivative valuation techniques are used for the calculation of the
strategy values. At this stage, we just intend to perform a qualitative analysis.
A detailed econometric analysis on realistic values for the assets is postponed
for future work.
Stochastic Volatility Models of Mean-Reverting Type Based on CARMA
Processes
N. Surulescu (University of Heidelberg)
We consider extensions of some classical mean-reverting stochastic volatility
models, the volatility being driven by a Continuous Autoregressive Moving
Average (shortly CARMA) process.
We derive some asymptotic formulae for the option prices and we give
estimators for the effective volatility. With the same technique, we also obtain
some estimations for the spot volatility and integrated volatility. These are
extensions of some results of Papanicolaou et al.
The problem of estimating the models parameters is also addressed.
Rank Reduction of Correlation Matrices by Majorization
R. Pietersz (Erasmus University Rotterdam / ABN AMRO), P.J.F. Groenen (Erasmus University Rotterdam)
In this paper a novel method is developed for the problem of finding a lowrank correlation matrix nearest to a given correlation matrix. The method is
based on majorization and therefore it has optimal convergence properties.
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The method is computationally efficient, is straightforward to implement,
and can handle arbitrary weights on the entries of the correlation matrix.
The problem of rank reduction of correlation matrices occurs when pricing
a derivative dependent on a large number of assets, where the asset prices are
modelled as correlated log-normal processes.
Semi-Lagrangian Time Integration for PDE Models of Asian Options
S. Rout (University of Greenwich), K. Parrott (University of Greenwich)
A variety of methods can be applied to the pricing of Asian options. Finite
difference methods are very flexible with regard to the asset price model, but
encounter difficulty when applied to PDE models of Asian options because
of the parabolic degeneracy in the average-price direction. Parrott and Clarke
showed how Semi-Lagrange (S-L) time-integration, developed for numerical
weather forecasting, is an elegant choice of technique which integrates out
the average price term and simplifies the finite difference equations into a parameterised Black-Scholes form. Boundary conditions are unnecessary in the
average-price direction. The implicit equations that result are unconditionally
stable, second order accurate and can be solved using standard tri-diagonal
solvers. Uniform meshes are not efficient however the S-L method is shown
to be easily applied in conjunction with coordinate transformations. The S-L
method is more effective with small number of time steps since it is increasingly diffusive as the number of time steps becomes large. Early exercise is
also easily incorporated, the resulting linear complimentarity problem can be
solved using a projection method. The S-L time integration method has been
shown to dramatically simplify the finite difference approximation of Asian
options. Second order accuracy has been confirmed for Asian options that
must be held to maturity. A comparison with published results for continuousaverage-rate Put and Call options, with and without early exercise, shows that
the method achieves basis point accuracy and that Richardson extrapolation
can also be applied.
Pricing options with discrete dividends by high order finite differences
and grid stretching in space and time
C.W. Oosterlee (TU Delft), C.C.W. Leentvaar (TU Delft), A. Almendral
Vazquez (Norwegian computing Centre)
In this talk, we present an accurate numerical solution to the Black-Scholes
equation with only a few grid points. Fourth and sixth order finite difference
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discretizations in space and in time are employed as well as grid stretching in
both direction by means of an analytic coordinate transformation.
Next to standard European options, the method is also evaluated for binary options (with discontinuous final conditions) and for problems with discrete dividend modelling (including a jump condition at dividend times). The
method presented will be a basis for the fast and accurate solution of high
dimensional partial differential equations dealing with multi-asset options.
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8:30–9:30 Plenary lecture
Charting Common Ancestry in Human Chromosomes (M. Waterman) . . . 194
9:30–10:00
10:00–12:00
BZ
Break
A multi-disciplinary survey on techniques used in communication theory
(I.C.C. de Bruin; theme: Aerospace) . . . . . . . . . . . . . . . . . . . .
(I.C.C. de Bruin) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Randomness in Wireless In-Home Networks (R. Rietman) . . . . . . . . . .
Matched layers in radio wave propagation modelling (E.R. Fledderus) . . . .
The impact of user mobility on wireless network planning (R. Litjens) . . . .
Numerical Simulations for Ultrasound Imaging and Inversion (R. Kowar;
theme: Life sciences) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A Fredholm integral equation in ultrasound imaging (R. Kowar) . . . . . . .
Nonlinear Ultrasound Wave Propagation in Thermoviscous Fluids (M.P.
Sørensen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
An Inverse Medium Problem in Scanning Acoustic Microscopy (C. Clason) .
Transmission Line Matrix Modeling of Sound Wave Propagation in Stationary and Moving Media (M. Bezdek) . . . . . . . . . . . . . . . . . . . .
Wavelets and its Applications I (H.G. ter Morsche) . . . . . . . . . . . . . .
Shape optimization using wavelet BEM (H. Harbrecht) . . . . . . . . . . . .
Hexagonal wavelets and the Dual Reciprocity method (H.G. ter Morsche) . .
Bayesian multiresolution analysis of Poisson count data with inhomogeneous
intensities (M.H. Jansen) . . . . . . . . . . . . . . . . . . . . . . . . . .
Wavelet analysis of sound signal in fluid-filled viscoelastic pipes (V. Prek) .
Modelling and simulation of industrial filtration and infiltration processes
I (O. Iliev) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Stochastic modelling and simulation of particle filtration in microstructures
(A.L. Latz) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vibration-assisted dead-end filtration: experiments and theoretical concepts
(M.A. Koenders) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modelling the cooling of beds of food products (P. Verboven) . . . . . . . .
Modelling of Filtration and Regeneration Processes in Diesel Particulate
Traps (U. Janoske) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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H4
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200 H 7
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Computational Mechanics organized by the ECMI SIG Multibody Dynamics (B. Simeon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205 H 7
Efficient application of implicit Runge Kutta methods for flexible multibody
dynamic systems (J. Gerstmayr) . . . . . . . . . . . . . . . . . . . . . . . 206
Simulation of shape memory actuators in robotics (G. Teichelmann) . . . . . 206
Integration of strongly damped mechanical systems by Runge-Kutta methods
(Th. Stumpp) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Using ODE Software for Problems in Computational Mechanics (B. Simeon) 208
Contributed presentations (theme: Electronic industry) . . . . . . . . . . . 208 H 11
Molten metal flow visualization using magnetic induction tomography(MIT)
based on level set method (M. Soleimani) . . . . . . . . . . . . . . . . . 208
Nonlinear Thermodynamics and Macrokinetics of Chemical Reactions and
Transport Phenomena (S. Sieniutycz) . . . . . . . . . . . . . . . . . . . . 208
Maximum entropy moment system of the semiconductor Boltzmann equation using Kane’s dispersion relation (V.R. Romano) . . . . . . . . . . . . 209
An improvement of SAINV and RIF preconditionings of CG method by
Double Dropping Strategy (S. Fujino) . . . . . . . . . . . . . . . . . . . 209
Numerical simulation of the problem arising in the gyrotron theory (J. Cepitis)210
A genetic algorithm for overnight LTL linehaul scheduling with small
amount of shipment (W.-J. Kim) . . . . . . . . . . . . . . . . . . . . . . 211
Contributed presentations (theme: Materials/Life Sciences/Water Flow) . . 211 H 12
Float Glass Process: Stability analysis in the presence of a large horizontal
temperature gradient (S.R. Pop) . . . . . . . . . . . . . . . . . . . . . . . 211
A Simplified Model for Non–Isothermal Crystallization of Polymers (T. Goetz)212
Design Optimisation of Wind-Loaded Cylindrical Silos Made from Composite Materials (E.V. Morozov) . . . . . . . . . . . . . . . . . . . . . . . . 213
Injection model in a porous medium with phase exchange (J. Pousin) . . . . 213
Droplet motion with phase exchange (J. Pousin) . . . . . . . . . . . . . . . 214
On 3-dimensional flows of stratified fluid in a homogeneous gravity field (A.
Giniatoulline) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
Contributed presentations (theme: Water flow) . . . . . . . . . . . . . . . . 216 H 13
Water flow influence to stability of subsoil and fundaments of dwelling buildings (P. Procházka) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
Finite Element Modified Method of Characteristics for Mean Water Flows:
Application to the Mediterranean Sea (M Seaid) . . . . . . . . . . . . . . 216
One approach to some steady and unsteady plane ideal fluid flow with free
surface (M.V. Polyakov) . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A Time-Split and Operator-Split Method for Reactive Flow in Porous Media
(H. Tawfiq) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
A finite-dimensional modal modelling of nonlinear resonant fluid sloshing
(A.N. Timokha) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218
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Deterministic extreme wave generation in a hydrodynamic laboratory (A.
Andonowati) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Charting Common Ancestry in Human Chromosomes
M. Waterman (University of Southern California)
Friday, 8:30–9:30, Blauwe Zaal
A reference human genome sequence is known with good accuracy, and variation among individuals is now of great interest. Variation can provide clues
to locate disease genes. In this lecture we develop dynamic programming
algorithms for haplotype block partitioning to minimize the number of representative single nucleotide polymorphisms (SNPs) required to account for
most of the haplotype quality in each block. The block quality is a function of
the haplotypes defined by the SNPs in the block. Any measure of haplotype
quality can be used in the algorithm and of course the measure should depend
on the specific application. The dynamic programming algorithm is applied
to analyze the haplotype data on chromosome 21 of Patil et al. (Science 294,
1719-1723 (2001)). Using the same criteria as in Patil et al., we identify a
total of 3,582 representative SNPs and 2,575 blocks which are 21.5% and
37.7%, respectively, smaller than those identified using a greedy algorithm of
Patil et al.
Minisymposium: A multi-disciplinary survey on techniques used in
communication theory
I.C.C. de Bruin (TI-WMC), E. Fledderus (TNO Telecom), R. Litjens (TNO
Telecom)
Friday, 10:00–12:00, Hall 5
The aim of this mini-symposium is to show similarities in theoretical, modelling and simulation aspects from seemingly different disciplines. All authors have a background in different areas of applied mathematics. The main
theme in all presentations is how knowledge from these areas: fluid dynamics, mobile, econometrics and systems theory, have been used in the relatively
young area of (mobile) communications, using the transversality of mathematics. In the remainder of this abstract, we focus on the four viewpoints
being considered in the mini-symposium.
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I.C.C. de Bruin (TI-WMC)
Friday, 10:00–10:30, Hall 5
In computational fluid dynamics, and in particular turbulence, one usually
has to find a trade-off in the way perturbations are superimposed on a base
flow: too extreme fluctuations are not realistic and may cause numerical instabilities, while in the other case patterns do not change fast enough and no
interesting features arise and simulations last forever. This paper will demonstrate how the random fluctuations used to generate turbulence in a turbulent
mixing layer, can also be used for the modelling of power, transmitted from a
stationary base station, and received by mobile phones moving past buildings.
In both cases, white Gaussian noise is imposed on a base signal in order to
model the behaviour. And in both cases the inclusion of spatial correlation
is crucial in order to come close to the real-life situation. Also the extension
to the generation of these fluctuations in more dimensions is already present
in the turbulence arena, while just a few studies exist in the area of mobile
communications.
Randomness in Wireless In-Home Networks
R. Rietman (Philips Research - CoSiNe group)
Friday, 10:30–11:00, Hall 5
Stochastic descriptions appear everywhere in science. Sometimes that is because, to the best of our knowledge, the process or system that we describe
really is stochastic, e.g. radioactive decay of an atom, but usually the randomness is used to describe our incomplete knowlegde of a process that we
think is really deterministic – e.g. tossing a coin.
The distinction between these two types of randomness could well be
purely philosophical and need not concern us here. What matters is that a
suitable description of a system may involve randomness.
An in-home WiFi system is presented as a nice playground for stochastics,
as it is an example of a system where many random processes come together
and interact:
-the wireless channel with fading and receiver noise
-the users and the data they send, interference
-the medium access protocol with random delays.
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Matched layers in radio wave propagation modelling
E.R. Fledderus (TNO Telecom), O. Mantel (TNO Telecom), D. Matic
(TNO Telecom), P. Pajovic (Technische Universiteit Eindhoven)
Friday, 11:00–11:30, Hall 5
The practical feasibility of the descriptions that exist for the decay of energy
of emitted radio waves is a trade-off between required accuracy, available data
of the environment and available computing infrastructure. Many mobile operators are currently perfectly satisfied with a stochastic model that has shown
its value when the mobile systems were designed. But with the upcome of
high-speed mobile data services, the cells in wireless systems shrink, possibly beyond the area where the stochastic models are valid. Other descriptions
than completely stochastic become more feasible, but can we relate the two
(or more!) descriptions, and where is the ‘boundary’ where one description
is ‘overtaken’ by the other? This boundary layer study has similarities with
modelling issues in fluid dynamics.
The impact of user mobility on wireless network planning
R. Litjens (TNO Telecom)
Friday, 11:30–12:00, Hall 5
The impact of mobility on radio network planning stems from two distinct
aspects. First of all, more severe signal-to-interference ratio requirements apply in case of higher terminal velocities due to e.g. multipath propagation
and transmission power control imperfections. Secondly, higher velocities
require a greater reservation of radio resources in anticipation of call handovers, in order to keep the probability of premature call termination below
a prespecified target value. As a consequence of this resource reservation,
fresh call blocking increases which induces a need for a denser planning of
base stations. We present an analytical approach in order to evaluate the impact of both these aspects on network planning, the rendered grade of service
and the associated investment costs. The strength of the presented analysis
lies therein that it is sufficiently realistic to provide valuable qualitative insight for network planning purposes, capturing the principal system aspects
of relevance, while it is simple enough to allow a computationally inexpensive evaluation and optimisation. A set of numerical experiments identify
terminal mobility as a key property that needs to be considered in the radio
network planning process and demonstrates the effectiveness of the investigated resource reservation scheme in reducing both the investment costs for
the mobile network operator and the grade of service as experienced by its
customers.
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Minisymposium: Numerical Simulations for Ultrasound Imaging and
Inversion
R. Kowar (University of Innsbruck), B.K. Kaltenbacher (University of
Erlangen-Nürnberg)
Friday, 10:00–12:00, Hall 4
Ultrasound imaging includes the following areas:
• classical ultrasound imaging (imaging of point scatterers),
• crack identification in metals,
• parameter estimation problems (estimation of material properties)
• static, dynamic and transient elastography,
• thermoacoustic or optoacoustic tomography and
• acoustic microscopy.
It is apparent that challenging mathematical problems appear in simulations of wave propagation and its inversions.
• Due to increasing computational power the simulations of sound phenomena became tractable. This limits the risk of testing new developments in engeneering design of medical devices and for non-destructive
evaluation.
• Novel inversion simulation techniques can be tested by combination of
experiments and numerical simulations, reducing developments costs.
The aim of this minisymposium is the modelling and the simulation of wave
propagation in continua and the estimation of material properties of continua.
A Fredholm integral equation in ultrasound imaging
R. Kowar (University of Innsbruck)
Friday, 10:00–10:30, Hall 4
Linear and nonlinear Fredholm integral equations are derived for the simulation of ultrasound wave propagation in tissues. Moreover these integral
equations can be used to estimaten density functions of tissues. By a density
function we mean a linear combination of the excess density function and
the excess wave speed function. In our models we neglect shear and viscosity forces. A linearized integral equation is investigated in more details for
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a zero-offset data configuration. We show that the inverse problem can be
decomposed in two inverse problems. The first inverse problem corresponds
to a set of one-dimensional integral equations with oscillating integral equation kernels. The second inverse problem corresponds to the inverse problem
of estimating the absorption function of electromagnetic waves. Finally we
present some numerical simulations.
Nonlinear Ultrasound Wave Propagation in Thermoviscous Fluids
M.P. Sørensen (Technical University of Denmark), A.R. Rasmussen (Technical University of Denmark), P.L. Christiansen (Technical University of
Denmark)
Friday, 10:30–11:00, Hall 4
Traditional ultrasound theory is based on linear theory. However, for strongly
focused sound beams, the pressure levels are sufficiently high to generate
nonlinear waves. In thermoviscous fluids nonlinearity arises as a result of a
nonlinear equation of state together with nonlinear advection. Furthermore,
dissipation and dispersion is included in a combined third order term in the
velocity potential.
We shall report on solitary pulse propagation with generation of higher
harmonics of the emitted carrier wave frequency. The envelopes of the carrier wave and its first higher harmonics satisfy two coupled nonlinear partial
differential equations, which resembles those of optical chi-2 materials. We
think this result makes a remarkable link between nonlinear acoustics and
nonlinear optics. Finally our analysis reveal an exact kink solution to the
nonlinear acoustic problem. This kink solution is interpreted as a shock wave
formation, similar in nature to those of the simple Burgers equation.
The results are relevant for medical ultrasound imaging.
An Inverse Medium Problem in Scanning Acoustic Microscopy
C. Clason (Technische Universität München)
Friday, 11:00–11:30, Hall 4
In applied material sciences imaging techniques based on ultrasound are established methods for the visualization of elastic properties. As a standard
tool for high resolution penetrating imaging of samples, the scanning acoustic microscope has proved to be a valuable instrument. This device uses a
moving acoustic lens to send out and record ultrasonic waves independently
at a number of points on a surface. The recorded signals are then used to
assign a grey value to each point, thus creating an image of the sample investigated. For medical applications, as for instance in objective control of the
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progress of bone formation after maxillo-facial surgery, quantitative evaluation of the measured data is of considerable interest. Our aim is to extend the
software of the microscope in cooperation with the manufacturer (KSI).
In order to obtain elasto-mechanical parameters of human bone, a mathematical characterization of the entire measurement process is necessary.
Apart from modeling the technical components of the microscope, the central
problem is to describe the interaction between the focused ultrasonic wave
and the specimen under investigation. Based on such a model the problem of
recovering these values can be cast into the form of identifying the unknown
space-dependent speed of sound in the three-dimensional acoustic wave equation.
Specific methods have to be devised for this kind of inverse medium problem, due to the complex nature of the boundary conditions and the reduced
set of measured data available. The parameter function can be recovered by
minimizing a suitable functional. Moreover, Tikhonov regularization can be
applied to obtain more stable results. Stability estimates support the choice
of functional.
Transmission Line Matrix Modeling of Sound Wave Propagation in Stationary and Moving Media
M. Bezdek (University of Erlangen-Nuremberg), H. Zhu (University of
Erlangen-Nuremberg), A. Rieder (University of Erlangen-Nuremberg)
Friday, 11:30–12:00, Hall 4
In this paper, simulation of sound wave propagation in stationary and moving
media is considered. The existing tools based on the finite element method
(FEM) often do not allow to perform a full 3D analysis due to an extensive
size of the acoustic domain. Furthermore, usage of the boundary element
method (BEM) is limited by unavailability of the appropriate Green’s functions. Therefore an alternative method is sought.
One such method, the transmission line matrix (TLM), is presented here.
TLM was originally developed to model electromagnetic wave propagation,
and later adopted in acoustics [1]. TLM is inherently a time-domain approach which does not require solution of a differential equation. It can be
regarded as a discrete realization of the Huygens’ principle. However, it can
be shown that TLM is numerically equivalent to the finite-difference timedomain (FDTD) discretization of the acoustic wave equation.
The functionality of TLM is demonstrated by means of various simulation
setups. Implementation of realistic acoustic sources and boundary conditions
in TLM models is considered. TLM and FEM are compared in terms of accuracy and computational complexity of the resulting models. It is concluded
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that TLM may represent a more efficient alternative to FEM when predicting
acoustic fields in stationary media.
Furthermore, applicability of TLM to moving media is examined. An extension of TLM has been recently proposed which allows to simulate sound
waves in 1D moving media [2]. Such waves are characterized by directiondependent propagation speed. In this paper, a TLM model of 2D moving
media is introduced. First simulation results are presented and validity of the
new TLM scheme is discussed.
[1] Kagawa et al.: Discrete Huygens’ Model Approach to Sound Wave Propagation,
J. Sound Vib., vol. 218, no. 3, pp. 419-444, 1998.
[2] O’Connor: TLM Model of Waves in Moving Media, Int. J. Numer. Model.,
vol. 15, pp. 205-214, 2002.
Minisymposium: Wavelets and its Applications I
H.G. ter Morsche (Technische Universiteit Eindhoven)
Friday, 10:00–12:00, Hall 7
Nowadays, wavelets (including the second generation wavelets) are used in a
broad spectrum of application areas like feature detection in images and signals, statistical analysis of time-dependent data, and computational methods
to solve partial differential equations, especially Boundary Element Methods.
The minisymposium Wavelets and its Applications will address some of these
areas. Among them are the detection of leaks in pipeline systems, the estimation of time-varying intensities of a Poisson count process, and the numerical
handling of shape problems in planar elasticity and electromagnetics.
Shape optimization using wavelet BEM
H. Harbrecht (University of Kiel), E.K. Eppler (WIAS)
Friday, 10:00–10:30, Hall 7
This talk is concerned with the numerical solution of shape optimization problems for linear elliptic boundary value problems. In particular, we treat shape
problems from planar elasticity and electromagnetics.
The underlying state function satisfies a Poisson equation on the actual
domain, the so-called state equation. For application of first and second order
optimization algorithms the state function itself as well as its higher order
normal and tangential derivatives must be computed.
The state equation has to be solved very often during the optimization
process. Therefore, fast methods are indispensible for its solution. We use
a boundary integral formulation which is solved by wavelet-based BEMmethods.
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Hexagonal wavelets and the Dual Reciprocity method
H.G. ter Morsche (Technische Universiteit Eindhoven)
Friday, 10:30–11:00, Hall 7
In the Dual Reciprocity Method (DRM) radial basis functions have been used
for computing a particular solution for an inhomogenuous partial differential
equation (pde). An important step in applying DRM is to construct a particular solution of the pde corresponding to the radial basis function itself. Thin
plate splines, Gaussians and multiquadrics are in general the most used radial
basis functions in this respect. However they all suffer from the fact that the
interpolation schemes involved are far from local and that for good approximations many shifts of the radial basis function are needed. It will be shown
that for the Poisson equation the so-called compactly supported hexagonal
wavelets could be good candidates to replace the radial basis functions. Despite the fact that the hexagonal wavelets are not pure radial symmetric, it is
still possible to derive a particular solution in a rather simple way. Moreover,
one has the general “compression” property that functions could be represented by wavelets relatively a few number of coefficients.
Bayesian multiresolution analysis of Poisson count data with inhomogeneous intensities
M.H. Jansen (Technische Universiteit Eindhoven)
Friday, 11:00–11:30, Hall 7
Many processes in physical, chemical and medical engineering generate Poisson count data with time (or space) varying intensities. The intensity curve
(as function of time or space) may show discontinuities. Multiscale methods
(wavelets) are particularly useful for the analysis of such piecewise continuous data. We present a general multilevel procedure to analyse and fit the data
in order to estimate the underlying intensities. A first element of this approach
is a so called Conditional Variance Stabilisation (CVS): the estimation of each
contribution (at given scales and locations) is performed, conditioned on the
sum of the observations related to that contribution. This conditional calculation has a normalising effect on the variances of the multiresolution (wavelet)
coefficients. A second element of this approach is a Bayesian framework
within the conditional calculations, consisting of a multiscale prior model,
also conditioned on the sum of the observed counts related to every wavelet
coefficient. The multiscale prior describes the relative input intensities as a
joint Dirichlet distribution.
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Wavelet analysis of sound signal in fluid-filled viscoelastic pipes
V. Prek (University of Ljubljana)
Friday, 11:30–12:00, Hall 7
In viscoelastic pipes, where the material properties depend on a complex
bulk modulus as well as on a complex shear modulus, the sound field within
the fluid is affected. Therefore, the dispersion of flexural waves occurs in
the pipe, while the speed of flexural waves decreases due to the coupled
fluid mass. Coupling between the pipe wall and the fluid also decreases the
sound speed in the fluid. Likewise, the speed of sound in fluid is frequencydependent, just as the group velocity of bending waves depends on the frequency. Wavelet transform of non-stationary sound signals was used to identify the frequency-dependent fluid sound speed. Measurement and analysis
of non-stationary signals with the use of time-frequency methods provides
a view to frequency dependent transfer characteristics of fluid-pipe coupled
systems. The so-called fluid mode and pipe mode resonant frequencies are evident and the impact of different pipe wall material properties is shown. The
results also showed that, in the case of propagating small disturbances (such
as acoustic waves), the pipe wall inertia has a minor influence on the wave
propagation characteristics. The elastic reaction of the wall to expansion of
the cross section greatly exceeds the inertial reactions.
Minisymposium: Modelling and simulation of industrial filtration and
infiltration processes I
O. Iliev (Fraunhofer ITWM), C. Koenders (School of Math. Kingston
Univ.), A. Latz (Fraunhofer ITWM)
Friday, 10:00–12:00, Hall 14
Modelling and simulation of filtration and of infiltration are essential for
optimizing a variety of industrial processes and environmental applications.
These include processes in the automotive industry, food industry, chemical
industry, waste water treatment, etc. Filtration and infiltration processes are
characterized by a wide range of space and time scales (from nanometers
to meters, from nanoseconds to days), and by a strongly coupled interaction of different forces and phenomena (free flow and flow in porous media,
species and/or particles transport, electrical forces, chemical reactions, biological processes, etc.)
The present minisymposium will emphasize the multiscale aspects, as well
as the treatment of strongly coupled processes. Models and algorithms for microscale (pore scale) and for macroscale filtration and infiltration processes
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will be discussed, together with certain upscaling strategies. Furthermore,
coupling of flow of the free fluid with the flow in the porous media, coupling
of flow with particles transport and adsorption, influence of time dependent
forces on filtration, etc., will be presented and discussed. Special attention
will be paid to discussion of efficient numerical methods for the considered
problems. Specific features of models and algorithms, associated with industrial filtration and infiltration processes will be outlined. The simulation and
analysis of a number of industrial processes will be presented and discussed
in detail, demonstrating how mathematical modelling assists in optimizing
these processes.
Stochastic modelling and simulation of particle filtration in microstructures
A.L. Latz (Fraunhofer ITWM)
Friday, 10:00–10:30, Hall 14
Many theories of particle filtration are based on simplified one-dimensional
considerations or on mathematical techniques like volume averaging and homogenization. In all these theories, it is implicitly assumed, that the filtration property of a complex microstructure can be quantified by a small number of macroscopic parameters. Comparisons with experiments are usually
very difficult since it is impossible to design filter media, which fulfil exactly
the requirements on statistical homogeneity, which are the basis for macroscopic theories. Direct simulation of particle motion and capture in complex
three dimensional microstructures is an alternative approach to study particle
filtration, which could not only be the sound basis for testing macroscopic
theories. It can also be used to study directly the dependence of filtration
properties on the real microstructure of the filter medium. Using concepts
from stochastic geometry it is possible to create realizations of random microstructures with unambiguously defined statistical properties. To calculate
the flow, we use a parallelized Lattice Boltzmann code, which was specifically developed for industrial applications at the ITWM. The motion of particles coupled to the flow is influenced first by the geometric randomness due
to the highly irregular microstructure, with which the particles are interacting by collisions and adhesion forces. Second there is the randomness of
the forces acting on small particles due to the thermal fluctuations within the
fluid. Both sources of randomness are accounted for by solving stochastic
differential equations for the motion of the particles with appropriate boundary conditions at contact with the microstructure. Since all simulations are
done in the full three-dimensional geometry, not only single fiber filtration
mechanisms (inertial impaction, Brownian motion, interception) but also the
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intrinsic three-dimensional mechanism of sieving of large particles is treated
within our approach.
Vibration-assisted dead-end filtration: experiments and theoretical concepts
M.A. Koenders (Kingston University)
Friday, 10:30–11:00, Hall 14
Dead-end filtration tests with a vertically vibrated medium are reported, focussing on the effect of acceleration amplitude. A phenomenological model
with constant coefficients and assumed constant solids volume fraction profile
is introduced. Its inadequacy in describing the subtleties of the experimental
data is discussed. A major shortcoming is the fact that a phenomenological
model cannot predict the solids volume fraction profile. A physical theory is
then reviewed in which the slurry is described as a dense gas with a positiondependent temperature. The theory is applied to the present problem. A nondimensional parameter S, which is proportional to the ratio of the mean fluid
velocity in the filter to the oscillation velocity amplitude, emerges from the
theory (gravitational effects are ignored). Using the physical theory, solutions
to the solids volume fraction profile are presented and their sensitivity to the
volume of solids in the apparatus and the parameter S are probed. Keywords:
dead-end filtration, vibrated medium, modelling, granular temperature theory
Modelling the cooling of beds of food products
P. Verboven (K.U. Leuven), E. Tijskens (K.U.Leuven), H. Ramon (K.U.Leuven)
Friday, 11:00–11:30, Hall 14
Packing of foods in boxes offers ease of handling and commercial benefits.
Cooling, however, is difficult because of air blockage by the box and expected
variation in airflow in between particles. Discrete element modelling was applied to simulate the filling of a box with spheres with a uniformly distributed
diameter between 65 and 75 mm. The air flow in the voids between the particles was solved by means of the non-structured finite volume CFD code
CFX5 on a PC workstation with 2 PIII 933 MHz processors. The simulations
revealed air flow channeling and consequences for heat transfer during cooling were investigated. Comparison to porous media models and measurement
was made. The presented model is a basis for box design, improved porous
medium models, and heat and mass transfer models of cooling of food items
in boxes. The use of real food shapes will be envisaged next.
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Modelling of Filtration and Regeneration Processes in Diesel Particulate
Traps
U. Janoske (University of Cooperative Education), T.D. Deuschle (University of Stuttgart), M.P. Piesche (University of Stuttgart)
Friday, 11:30–12:00, Hall 14
The reduction of exhaust particulate emissions from diesel vehicles is a great
upcoming challenge. As a result of their harmful effects, new legislation
on diesel vehicles has been introduced throughout the world specifying low
emission-levels. Today, the use of diesel particulate filter (DPF) in addition
to engine modifications is the favoured method to fulfil these criteria. The
principle of a DPF is based on the accumulation of particles in the alternating open and closed channels of the filter. The pressure drop over the DPF
increases with time. This increase is associated with the rise of fuel consumption. For this reason, the deposited filter cake must be occasionally regenerated. To minimise complex and expensive investigations on test benches, a
mathematical model has been developed describing the loading and regeneration behaviour of a DPF. The model is integrated in a commercial CFD-Code
using user-defined subroutines (UDS). The CFD-Code was used for the calculation of the fluid flow and the particle tracks of different kinds of particles
(e.g. soot, additives) in a two-dimensional model of the DPF. Thus, the axial
and radial structure of the deposited particles on the filter can be determined.
In the UDS models are implemented to calculate the pressure loss, the separation efficiency and the regeneration behaviour. Comparing the simulation
results with the results gained experimentally, it can be seen that both sets of
data concur. Further development concerning the implementation of a subroutine to describe the long-term behaviour and transport of the deposited
particles will be carried out.
Minisymposium: Computational Mechanics organized by the ECMI
SIG Multibody Dynamics
B. Simeon (Munich University of Technology)
Friday, 10:00–12:00, Hall 7
The minisymposium on Computational Mechanics covers a rapidly developing field where numerical simulation has become a key technology. Typical
applications in this field are the industrial design of road and railway vehicles,
of robots, and of air- and spacecrafts. Organized by the Special Interest Group
Multibody Dynamics of ECMI, this minisymposium provides an interdisciplinary forum for the exchange of research results and strives to stimulate the
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collaboration between academic and industrial research groups. Among the
topics presented are new numerical algorithms, FEM coupling with multibody dynamics software, and applications in robotics.
Efficient application of implicit Runge Kutta methods for flexible multibody dynamic systems
J. Gerstmayr (Johannes Kepler University of Linz)
Friday, 10:00–10:30, Hall 7
Fully implicit Runge Kutta methods, such as Gauss, Radau or Lobatto
schemes are known to have best conditions for highest consistence order or
stability with respect to the number of integration points. In the case of differential algebraic equations, Radau IIA methods can be used in order to solve
problems with index 3 without prior index reduction. The disadvantage is
certainly the higher effort for solving nonlinear equations for every timestep.
It will be shown that high order integration methods perform well compared
to the well known multistep methods. Two different formulations for flexible
multibody systems are preferably used. First, the floating frame of reference
formulation (FFRF), where highly nonlinear inertia terms result from the additive decomposition into flexible and rigid body coordinates. The computational effort is reduced, if the mass matrix is not inverted during the derivation
of the equations of motion. In the case of a modified Newton scheme, the effort for the computation of the Jacobian can be kept independent from the
number of stages if the number of elastic coordinates dominates the problem compared to algebraic constraints. In industrial multibody systems, the
number of unknowns for a flexible multibody system is frequently not exceeding several hundreds, and therefore the factorisation of the Jacobian after
every update is less costly than the computation of the residual in every iteration. As a second approach, the absolute coordinate formulation (ACF) is
presented which has advantages with respect to the reduction of the number of
algebraic terms for the equations of motion and with respect to a linearization
of the nonlinear stiffness matrix. Certain disadvantages, like the more difficult formulation of constraints have been addressed in the recent literature on
the absolute nodal coordinate formulation. Both formulations are compared
and numerical examples as well as convergence studies are presented.
Simulation of shape memory actuators in robotics
G. Teichelmann (Technische Universität München)
Friday, 10:30–11:00, Hall 7
Shape memory materials are in use in different fields of application like aviation or medicine. In robotics they can be used as temperature controlled
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actuators and allow the design of quite small manipulators. Yet the computational simulation of shape memory materials is in focus of research and far
from maturity. Here a mathematical model that is able to reproduce the main
phenomenological aspects of shape memory behaviour like one- and two-way
effects as well as pseudoelasticity and pseudoplasticity will be presented. It
is composed of a state- and temperature- dependent set of evolution equations
that describe the local material properties by internal variables. For the global
simulation of a component a structural mechanics model is used, which forms
a system of partial differential algebraic equations and is discretized in space
by finite elements. After regularization it results in an ordinary initial value
problem. The computational concepts like dynamical integration by standard
ode-solvers or the solution of the associated quasistationary problem still face
some difficulties. They will be outlined by an example of a simple one dimensional shape memory wire.
Integration of strongly damped mechanical systems by Runge-Kutta
methods
Th. Stumpp (University of Tübingen)
Friday, 11:00–11:30, Hall 7
Strongly damped mechanical systems arise, for example, in vehicle dynamics and in modelling joints in biomechanics. Standard explicit integrators become unstable unless very small time steps are chosen. We are interested in
the numerical solution of such systems with step sizes that are independent of
the damping parameter. The associated equations of motion are represented
by a second order differential equation with a small parameter ε,
M(y) ÿ = f (y, ẏ) −
1
D(y) ẏ,
ε
where the strong damping forces are represented in a positive semi-definite
damping matrix D(y).
Concerning the qualitative behaviour, it will be shown that the strong
damping forces solutions to run rapidly into an invariant manifold. The
smooth motion of the mechanical system on this manifold is expanded in
terms of solutions of differential-algebraic systems of index 2. These results
hold for analytical solutions as well as for numerical solutions of suitable
methods such as Radau collocation. For ε → 0 it turns out that the error of
numerical solutions of the strongly damped mechanical system obtained with
step sizes h > ε is bounded by errors for the differential algebraic systems.
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Using ODE Software for Problems in Computational Mechanics
B. Simeon (Munich University of Technology)
Friday, 11:30–12:00, Hall 7
The talk discusses the pros and cons of using ODE software for timedependent PDEs and coupled problems in computational mechanics. Two
examples, flexible multibody dynamics and elastoplasticity, illustrate the potential and the limits of standard codes in this field. As it turns out, the interplay of space and time discretization needs a careful treatment both from the
theoretical as well as the software point of view.
Contributed presentations (theme: Electronic industry)
Molten metal flow visualization using magnetic induction tomography(MIT) based on level set method
M. Soleimani (UMIST), W.R.B. Lionheart (UMIST)
Friday, 10:00–10:20, Hall 11
In MIT an alternative current passes from excitation coil, creates eddy currents eddy currents can be detected by sensing coils. These sensing induced
voltages can be used as the data for the conductivity imaging. The forward
problem is to simulate this measurement process. The inverse problem is
the conductivity reconstruction using the measurement data. There has been
growing interest in the development and use of geometrical inversion methods, which moves away from the estimation of a dense collection of pixel
values and concentrate processing resources directly on the recovery of information regarding anomalies. We reformulate the problem of the conductivity
reconstruction to a special geometrical representation of the objects. Level
set method (LSM) and a velocity function is derived to evaluate moving of
the boundaries. The numerical implementation in 3D_MIT using a forward
model developed using edge FEM and an inverse solver using LSM will be
shown.
Nonlinear Thermodynamics and Macrokinetics of Chemical Reactions
and Transport Phenomena
S. Sieniutycz (Warsaw University of Technology)
Friday, 10:20–10:40, Hall 11
We consider mathematical structures describing rates of chemical reactions
and transport processes in nonlinear diffusion-reaction systems. By analyzing
two competing processes in an elementary diffusive-transport step we show
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209
that disequilibrium rates are described by nonlinear equations exponential
with respect to the Planck potentials and temperature reciprocal. Simultaneously these equations are analytical expressions characterizing the transport
of substance or energy through the energy barrier. We regard these kinetics
as potential representations of generalized law of mass action that includes
transfer phenomena, external fields, nonlinear symmetries and generalized
affinity. We show the correspondence with the classical kinetics near equilibrium. Our generalized affinities provide an alternative to usual driving
forces in non-equilibrium transport processes. The field counterpart of the
theory implies that diffusion coefficients are not constants but are exponential functions of intensive state coordinates. We quote remarkable number
of experiments confirming such nonlinear behavior in practical or industrial
systems.
Maximum entropy moment system of the semiconductor Boltzmann
equation using Kane’s dispersion relation
V.R. Romano (Universitá di Catania), M. Junk (Universität Kaiserslautern)
Friday, 10:40–11:00, Hall 11
The direct integration of the transport equation coupled to the Poisson equation for the description of the motion of charges in semiconductors is a daunting computational task. Since one usually is not interested to the complete details of the distribution function but to quantities as average electron density,
energy, velocity, several macroscopic models for charge transport in semiconductors have been developed. These models are based on the moment systems
arising from the Boltzamn equation and require suitable closure assumptions.
A physically sound way to get the sought closure relations is based on the
maximum entropy principle (MEP).
From a mathematical point of view MEP gives an approximation of the
exact distribution function in terms of a finite number of moments and require
to solve a constrained optimization problem. However this latter does not
always admit solution as in the case of gas dynamics and for semiconductors
when. the parabolic approximation is used for the energy band of electrons.
The main goal of the present article is to show that such a problem is overcome when one employs the Kane model for the energy band. It is proved
that the corresponding maximum entropy models are symmetric hyperbolic
system in a convex domain and that the equilibria are interior points, guaranteeing the validity of expansions around equilibrium states.
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Friday Morning
An improvement of SAINV and RIF preconditionings of CG method by
Double Dropping Strategy
S. Fujino (Kyushu University)
Friday, 11:00–11:20, Hall 11
Preconditioning based on incomplete factorization of the matrix A is among
the best known method for solving a linear systems with SPD matrix. However, the existence of an incomplete factorization is a delicate issue. Stabilized AINV and RIF preconditionings with single dropping have been proposed. Dropping is a key to improvement of efficiency. A new dropping
strategy of both SAINV and RIF will be proposed. We show numerical results of preconditioned CG methods for structural analysis with unknowns of
10626.
its.
time(sec.) ratio
CG
div.
ICCG 7620
102
1.0
Table:
31.2
.31
SAINVCG 3166
*ISAINVCG 1468
11.2
.11
RIFCG 1735
15.8
.16
*IRIFCG 447
6.2
.06
We can see that the improved SAINV and RIF (marked with * in Table)
perform well in terms of CPU time and iterations.
Numerical simulation of the problem arising in the gyrotron theory
J. Cepitis (Institute of Mathematics, LAS and UL), O. Dumbrajs (Helsinki
University of Technology), H. Kalis (Institute of Mathematics, LAS
and UL)
Friday, 11:20–11:40, Hall 11
Gyrotrons are microwave sources whose operation is based on the stimulated
cyclotron radiation of electrons oscillating in a static magnetic field. The
mathematical modelling of gyrotron processes we carried out because of paper [1].
Assuming the estimates 0 ≤ | p|2 ≤ 1 for the dimensionless complex transverse momentum of the electron p we obtain that non-stationary gyrotron oscilations for every mode can be described by the integro-differential equation
i
∂2g
∂g
= 2 + δg − i I
∂t
∂x
Z
x
g(ξ, t) exp(i1(ξ − x))dξ,
0
where i is the imaginary unit, the unknown function g is the high-frequency
field in resonator depending on the normalized axial space and time coordi-
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211
nates x and t, δ classifies variation of the critical frequencies, 1 is the frequency mismatch and I is the dimensionless current.
The numerical simulation in the case I = 0 for this equation supplemented
by the standard initial condition and the boundary conditions for the field
at the entrance and at the exit to the interaction space was investigated in
the paper [2]. At present we have completed results as well for the general
case. Particularly, the two level finite-difference schemes with uniform grid
and various types of non-uniform grid were applied and the relevant results
compared. Simultaneously, the quasistationary solutions and corresponding
eigenvalues and eigenfunctions of the arising problem were investigated.
[1] M.I. Airila and O. Dumbrajs. Generalized gyrotron theory with inclusion of adiabatic electron trapping in the pressence of a depressed collection. Phys. Plasmas
8, 1358-1362 (2001).
[2] O. Dumbrajs, H. Kalis and A. Reinfelds. Numerical solution of single mode
gyrotron equation. Mathematical Modelling and Analysis 9, 25-38 (2004).
A genetic algorithm for overnight LTL linehaul scheduling with small
amount of shipment
W.-J. Kim (Seoul National University of Technology), S. Lee (Sangwook), S. Park (Soondal)
Friday, 11:40–12:00, Hall 11
Overnight LTL linehaul scheduling is to determine the vehicle routing to
move all shipment from its originating terminal to its destination terminal.
The transportation system having a different transshipment point for each
pair of terminals is efficient for overnight LTL linehaul scheduling with small
amount of shipment since small amount of shipment can be consolidated and
moved by a vehicle. The purpose of this paper is to develop an efficient genetic algorithm for the transportation system. It is suggested how to generate
a chromosome for representing transshipment points and how to evolve the
chromosome by reproduction, crossover, and mutation operations. A heuristic method is developed for making roundtrips as many as possible with the
transshipment points and for reducing total driving mileages. The computational results show that our algorithm is superior to the general genetic algorithms.
Contributed presentations (theme: Materials/Life Sciences/Water Flow)
Float Glass Process: Stability analysis in the presence of a large horizontal temperature gradient
212
Friday Morning
S.R. Pop (Fraunhofer ITWM)
Friday, 10:00–10:20, Hall 12
Float glass is a term for perfectly clear, flat glass (basic product). As the
formation of the thin glass ribbon takes place in a molten tin bath, it is considered that the flow and heat transfer induced there, are partially responsible
for the loss in the optical quality.
In this paper we examine the instabilities that can cause the small disturbances to appear at the interface between glass and metal. We consider the
free surface mixed convection problem of two superposed immiscible, incompressible fluids in two dimensions. The fluids are moving with different
velocities: the speed of the glass is given by the speed of the rollers that
stretch it, whereas the buoyancy effects cause the movement of the molten
tin. Assuming a large horizontal temperature gradient, we examine the problem by means of small perturbation analysis. Considering a base flow profile,
for the velocity (emphasizing the mixed convection of the tin and having a
Couette-Poiseuille profile for the glass) and the temperature (which is a linear function), with the free surface as a straight line, we disturb the flow using
small perturbations. Thus, we obtain a system of two Orr-Sommerfeld equations coupled with two energy equations, and general interface and boundary
conditions. We solve the system analytically in the long waves limit and also
using small waves approach for the short waves limit. The system is solved
numerically using modified Keller-Box method. We show the existence of
the small-amplitude traveling waves, which move with the constant velocity
for wavenumbers in the medium range. We analyze the stability for a wide
range of wavenumbers, Reynolds and Grashoff number, and explain the physical implications of the dynamics of the problem and the difference from the
classical instabilities (Kelvin-Helmholtz, Holmboe). The consequences of the
linear stability are discussed.
A Simplified Model for Non–Isothermal Crystallization of Polymers
T. Goetz (University of Kaiserslautern), J.S. Struckmeier (University of
Hamburg)
Friday, 10:20–10:40, Hall 12
Recently, Burger and Capasso [M3 AS 11 (2001) 1029–1053] derived a coupled system of partial differential equations to describe non–isothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth–and–growth process describing the nucleation and
growth of single crystals. In the present work we reconsider the scaling properties of the dimensional system as well as some special one–dimensional
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models. Moreover, using an appropriate scaling of the original system, we derive a simplified model which only consists of a reaction–diffusion equation
with memory for the underlying temperature, such that the degree of crystallization can be explicitly given by a time integration of the temperature–
dependent growth and nucleation rate. Numerical simulations indicate that
the reduced model shows at least qualitatively the same behavior like the
original model.
Design Optimisation of Wind-Loaded Cylindrical Silos Made from Composite Materials
E.V. Morozov (University of KwaZulu-Natal)
Friday, 10:40–11:00, Hall 12
The conventional material from which silos are usually constructed is steel,
and the existing codes and standards on these structures reflect the design criteria appropriate for an isotropic material. This paper deals with the design
optimisation of the silos made from composite materials. The purpose of the
present study is to perform the design optimisation of cylindrical composite
silos loaded with the unsymmetrical external pressure caused by the action of
wind. The material that is considered for the cylindrical shell part of the silo is
a laminate, consisting of the helical and hoop layers. The design variables are
the helical angle, and thicknesses of the layers. The objective function of the
design optimisation is the total thickness of the wall (which determines the
weight and effectively the cost). The buckling constraint due to wind loading
is imposed on the design variables. The relevant data for the particular design
example considered in this study are: silo height = 7000 mm, diameter = 2600
mm. The minimum design values for the layer thicknesses corresponding to
these data and wind velocity of 100 km/h were found using the numerical
construction of the limiting critical surface of buckling. The limiting surface
was built up using finite element buckling analysis combined with the numerical search of the optimum parameters. The minimum thickness occurs for h
= 1.28 mm. The maximum total thickness lying on the design surface is h =
1.8 mm, which is 29% higher than the minimum value.
Injection model in a porous medium with phase exchange
J. Pousin (INSA de Lyon), E.Z. Zeltz (INSA de Lyon), A. M. Mikelic
(Université C. Bernard)
Friday, 11:00–11:20, Hall 12
In accidental situations a concrete wall can be stricken with a hight temperature stream of vapor. For studying the impact of a vapor stream impinging
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a conrete wall, we propose a 3D homogenized model when the stream is stationary and when the surface tension at the interface vapour/residual fluid is
neglected. We prove that the interface evolves as a (shock or detent) wave
accordingly with the mobility coefficient values M. We prove the existence
of a finite asymptotical position for the interface when t goes to +∞.
Starting from the model developed in [1], we introduce the change of phase
and we prove that for a single pore the function a : (x2 , t) 7−→ z = a(x2 , t)
describing the interface between the residual fluid and the vapor verifies:

!

∂
f M (a(X 2 , t))
 ∂a(X 2 , t)
+q
= 0 in ]0, +∞[×]0, T [
∗
∂t
∂ X2
1 + δ2 t


ad = a(X 2 , 0) = 12 for X 2 > 0; ag = a(X 2 , 0) = 0 for X 2 < 0
(13.1)
with X 2 = x2δ∗ , have been used. Here δ ∗ represents the fraction of vapor
1+
2
t
pvs (T )
which is condensed and is given by ([2]) δ ∗ = pi −
pvs (T ) and is supposed to
be small.
During this presentation, the numerical results obtained with our model
will be compared with experimental results given in [3].
[1] A. Maazouz, A. Mikelic, J. Pousin, E. Zeltz: Fluid injection model without
surface tension for resins in thin molds, Journal of Comp. and Appl. Math
(2004)doi:10.1016/S0377-0427(03)00498-9.
[2] Martin E. R. Shanahan: Is a Sessile Drop in an Atmosphere Saturated with Its
Vapor Really at Equilibrium. Langmuir Letters, Vol. 18 n◦ 21 (2002), p. 77637765.
[3] M. Shekarchi, G. Debicki, L. Granger, Y. Billard: Study of leaktightness integrity
of containment wall without liner in high performance concrete under accindental
conditions-I. Experimentation, Nuclear Engineering and Design, Vol. 213 (2002),
pp. 1-9.
Droplet motion with phase exchange
J. Pousin (INSA de Lyon), A.M. Mikelic (Université C. Bernard), T. C.
Clopeau (Université C. Bernard)
Friday, 11:20–11:40, Hall 12
The efficiency of Genechip probe arrays relies on the ability to fix uniformly
probes on a plane surface in a localized way. To do so, an industrial process
consists in projecting on the plane surface liquid droplets made of a volatile
solvent containing the probes to be fixed. The localization will be obtained
through a treatment of the plane surface such that some parts of it are repulsive
for the solvent chemical species some others not.
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During this presentation, we will discuss a mathematical model for describing the motion of a droplet on a plane when vaporization occurs. This mathematical model is based on the works of [3], [1] for the physical aspects of
vaporization, and on the work of [2] for the angle contact law. If a, h, V , and
λ are functions representing respectively the triple contact line, the height of
the droplet, the volume of the droplet and an auxiliary function, these functions are solution to an PDF system. The system is integrated numerically,
and the results are compared with experimental results.
[1] R.D. Deegan, Olgika Bakajin, Todd. F. Dupont, Greg Huber, Sidney R. Nagel
and Thomas A. Witten. Contact line deposits in an evaporating drop, Physical
Review E. 62 (1) (2000) p. 756-765.
[2] P.G. de Gennes. Wetting: statics and dynamics, Reviews of Modern Physics, 57,
(1985), p. 827-863.
[3] Martin E. R. Shanahan. Is a Sessile Drop in an Atmosphere Saturated with Its
Vapor Really at Equilibrium. Langmuir Letters, 18 n◦ 21 (2002), p. 7763- 7765.
On 3-dimensional flows of stratified fluid in a homogeneous gravity field
A. Giniatoulline (Los Andes University)
Friday, 11:40–12:00, Hall 12
We consider the system which describes small displacements of an exponentially stratified viscous fluid in the gravity field

∂p
1
ρ∗ ∂u


∂t − µ1u 1 + ∂ x1 = 0


∂p
∂u 2


 ρ∗ ∂t − µ1u 2 + ∂ x2 = 0
∂p
3
ρ∗ ∂u
(1)
∂t − µ1u 3 + gρ ∂ x3 = 0 .

g

∂ρ

−
u
=
0

3

N 2 ρ∗ ∂t


∂u 3
∂u 1
∂u 2
+
+
∂ x1
∂ x2
∂ x3 = 0
For (1), we establish the properties of existence and uniqueness of the solutions, the dissipation of energy of internal waves, and investigate the localization and structure of the spectrum of normal vibrations. From different points
of view, we consider a remarkable analogy between stratified flows described
by (1), and rotational flows governed by the system (2):
( −
→
−
→
−
→ −
∂→
u
∂t + ω × u − µ1 u + ∇ p = 0
(2)
∂u 3
∂u 1
∂u 2
∂ x1 + ∂ x2 + ∂ x3 = 0
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Friday Morning
Contributed presentations (theme: Water flow)
Water flow influence to stability of subsoil and fundaments of dwelling
buildings
P. Procházka (CTU Prague, Civil Engineering), V. Dolezel (Technical
University)
Friday, 10:00–10:20, Hall 13
Mathematical formulation of the problem will be established and solution of
the free hexagons based on the boundary element method will be discussed. A
special technique of the boundary element method will be used together with
a discrete element method to enable one to express a nonlinear behavior of a
part of the subsoil of a surface loading (with primarily application to dwelling
buildings). Another possible application in geotechnics - slope stability - will
demonstrate typical application of the approach discussed. To improve material properties of the subsoil or slopes, coupled modeling (mathematical and
scale modeling) will be used. Scale modeling starts with physically equivalent materials prepared in stands - glassed boxes of the sides of about 2 x 2 x
2 cubic meters. The material for the experiments is prepared in such a way it
obeys similarity rules. One paper will be presented with my graduate student.
Finite Element Modified Method of Characteristics for Mean Water
Flows: Application to the Mediterranean Sea
M Seaid (TU Darmstadt), M. Gonzalez (Oceanografia y Medio Ambiente)
Friday, 10:20–10:40, Hall 13
We present a new numerical method for solving unsteady free surface water flows. The method consists of an Eulerian-Lagrangian splitting of the
equations along the characteristic curves. The Lagrangian stage of the splitting is treated by a modified method of characteristics, while a finite element
method is used for the Eulerian stage. The combined two stages turn to a robust algorithm for solving accurately the equations and also overcome many
difficulties in other numerical method to treat the advective part of the free
surface equations.
Our contribution is mainly focused in the two-dimensional shallow water
equations used to model the mean water flow through the street of Gibraltar.
These equations are highly nonlinear and coupled equations with Coriolis
force and viscosity effect. In order to avoid any restriction on the size of
timesteps in the diffusive stage of the algorithm, and also to reduce numerical
dissipation we propose a linearly implicit scheme for the time integration.
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The algorithm is first tested for some simple benchmark problems used in
the literature to test the accuracy of characteristic-based methods. Then, we
show results obtained for the mean water flow in the street of Gibraltar. Comparisons to measurements on the strait are also given in our contribution. For
our computations we used bathymetric data recently provided by the University of Malaga in Spain.
One approach to some steady and unsteady plane ideal fluid flow with
free surface
M.V. Polyakov (Dniepropetrovsk National University), D.V. Yevdokymov
(Dmytro)
Friday, 10:40–11:00, Hall 13
Last decades a lot of papers were devoted to free surface problem, most of
them where based in the ideal fluid flow model. From a mathematical point of
view the corresponding boundary-value problems are formulated as moving
boundary problems (unsteady case), or unknown boundary problems (steady
case), and they contain specific form of non-linearity. Boundary integral
equations are effectively used for numerical solution of that kind of problems.
However a difficulty arises during solution of the considered problems for
non-vortical flows in plane case, because the velocity potential loses uniqueness in this case due to circulation around airfoils the flow. On the other hand,
the free surface boundary condition in unsteady ideal fluid flow is usually
formulated as Cauchy-Lagrange integral, that is it used the velocity potential.
Stream function formulations is considered in the present work. The flow on
surface can be assumed potential and Cauchy-Lagrange integral takes place
there. The main idea of the present work is replacement of velocity potential
in Cauchy-Lagrange integral by stream function, using well-known relations
between velocity potential and stream function. Steady and unsteady plane
free surface flows are considered using stream function formulation. Euler
type time-stepping scheme is used for calculation of free boundary motion
and for calculation of stream function boundary conditions from the CauchyLagrange integral. Boundary element method is used for numerical solution
of boundary-value problems on every time step in unsteady case and on every
iteration step in steady case. The proposed approach is illustrated by several
examples of numerical solution of the mentioned problems. Since there is not
analytical solutions of such kind of non-linear problems, the indirect checking procedure, based on comparison of calculation with different boundary
element grids, is used for that aim.
218
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A Time-Split and Operator-Split Method for Reactive Flow in Porous
Media
H. Tawfiq (KFUPM)
Friday, 11:00–11:20, Hall 13
The shape stability of the reaction interface for the reactive flow in porous
media is modeled mathematically by a nonlinear system of coupled flow,
transport, and reaction equations. The nonlinear coupling between flow and
transport, due to porosity change, added more difficulties to the system. The
porosity changes occur due to reaction with the solid components and may
lead to fingering instabilities. We present a numerical model for this problem
which we refer to as Reaction-Infiltration Instability problem. The numerical model uses a mixed finite element method for flow and a Godunov-mixed
method for transport. A time-splitting approach decouples the system and requires the solution of only linear equations. Optimal order a priori error estimates for the discretization of the coupled nonlinear system and the operatorsplitting error are derived. Numerical studies to verify analytical results and
to test the performance of the method on heterogeneous media are presented.
A finite-dimensional modal modelling of nonlinear resonant fluid sloshing
A.N. Timokha (Jena University), M. Hermann (Jena University)
Friday, 11:20–11:40, Hall 13
Steady-state and transient resonant wave patterns of fluid sloshing in moving tanks with finite depths are constituted by contribution from a little set
of natural modes. These leading modes are involved in nonlinear interaction. Remaining modes furnish smaller asymptotic supplement captured
with linear sloshing theory. This smart physical fact hides in background
of finite-dimensional mathematical modelling of fluid sloshing. Approximate solutions of the original free boundary value problem are found from a
finite-dimensional system of nonlinear ordinary differential equations (modal
system) coupling time-dependent amplitudes of the leading modes (modal
functions). Derivation of these modal systems is typically based on combining projective and asymptotic schemes. Ordering the leading modes as
1/k , k ∈ N ( is the non-dimensional amplitude of external harmonic excitation) determines structure and dimension of the modal systems. Double purpose of this talk is to give both a detailed survey and an extensive comparative
analysis of various existing modal systems dealing with two-dimensional resonant fluid sloshing in a harmonically shaken rectangular rank. The main emphasis is placed on bifurcations of asymptotic and numeric steady-state (periodic) solutions of multi-dimensional modal systems. Non-typical secondary
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bifurcations are reported for single-dominant theory based on the Moiseyev
asymptotics. This finding may physically indicate either failure of singedominant modal modelling outside of an admissible frequency-amplitude domains or requirement in modifying the Moiseyev asymptotic ordering. The
modification consists of accounting internal resonances leading to amplification of higher modes. Some existing multidimensional asymptotic modal
systems capturing internal resonances are discussed.
Deterministic extreme wave generation in a hydrodynamic laboratory
A. Andonowati (Institut Teknologi Bandung (ITB))
Friday, 11:40–12:00, Hall 13
This research is motivated by the requirement of hydrodynamics laboratories
to generate extreme waves for testing ships in steep, large amplitude wave
fields. Because of the physical limitations, direct generation of such waves is
not possible. An input signal given to the wave maker will deform, and the
amplitude can increase, while propagating down streams. Exploiting this fact,
then given a position in the wave tank of a test object, it is desired to determine
an input signal so that at this position a large amplitude wave emerges.
In order to address this deterministic extreme wave generation, we use the
concept of the Maximal Temporal Amplitude (MTA). This quantity measures
at each downstream position the maximal amplitude of the time signal of the
nonlinearly evolving wave. The applicability and relevance of this concept
has been shown for the propagation of a signal that is bi-chromatic at the
wave maker. For this case the MTA-curve showed accurately the position
where the largest deformation take place, and provided information on the
amplitude amplification factor in comparison to the original signal.
Aiming to find even more extreme waves, we will exploit an exact solution
of the spatial NLS that is known as the Soliton on Finite Background (SFB).
A characteristic of SFB is that wave focusing takes place leading to time periodic extreme waves in between phase singularities. For a given modulation
length of SFB and desired maximum amplitude at a position in a tank, the
MTA readily shows the maximum signal that is required at the wave maker
and the amplitude amplification factor of the requested signal. Some examples of the generation in realistic laboratory situations will be treated. Comparison with numerical results using a fully non-linear wave generation code
will be presented.
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Friday Afternoon
13:00–14:00
Plenary lecture
The MEGAFLOW Project: Numerical Flow Simulation of Complete
Transport Aircraft (C. Rossow) . . . . . . . . . . . . . . . . . . . . . . . 222
14:00–14:15
Break
14:15–16:15
BZ
Mathematical Tools of Signal Analysis in a Context of Increasing Complexity. (F. Nekka; theme: Materials) . . . . . . . . . . . . . . . . . . . . . . 223 BZ
Classification of Multiplicative Cascades: The Need to Modify the Usual
Autocorrelation Function. (L. Li) . . . . . . . . . . . . . . . . . . . . . . 223
New Strategies for Texture Analysis of Different Complexity Degrees. (F.
Nekka) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Multi-fractal Analysis of Indian Rainfall Data (A.H. Siddiqi) . . . . . . . . . 224
Wavelets and its Applications II (A.S. Tijsseling) . . . . . . . . . . . . . . . 224 H 7
Wavelet application for leak detection in water distribution systems (A.R.
Simpson) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
Wavelet analysis of transients in pressurized pipes and leak detection (M.
Ferrante) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Cross correlation, Wavelet and Cepstrum analyses for identifying reflection
points in pipeline networks. (S.B.M. Beck) . . . . . . . . . . . . . . . . . 226
Overview of Leak Detection Methods and Application in the Field (H. Ramos)226
Modelling and simulation of industrial filtration and infiltration processes
II (O. Iliev) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227 H 14
On efficient simulation of 3D flows of liquids through industrial filters (O.
Iliev) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Mathematical Modelling Of Flow Through Pleated Cartridge Filters (V.
Nassehi) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 228
Net Campus for Modelling Education and Industrial Mathematics (M.
Heiliö) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 H 12
Web Based Education of Mathematical Modelling - A Case Report. (S.A.
Pohjolainen) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 230
E-Learning Simulation: Creation and Delivery of Interactive Learning Object in the Mathematical and Physics Didactical Domain (G. Iovane) . . . 230
A web supported Applied Mathematics course (G. Faraco) . . . . . . . . . . 231
An Integrated Framework for Web Publication of Interactive Documents
(A.M. Anile) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231
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Towards a European Net Campus for Industrial Mathematics (M. Heiliö) . . 232
A system for distance graduate studies and scientific cooperation in the Internet environment; development and applications (J. Mockus) . . . . . . 232
Contributed presentations (theme: Aerospace) . . . . . . . . . . . . . . . . 233
Application of visco-plastic behavior of composites - bounds on overall properties (P. Procházka) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
On the application of least-squares reconstruction in the computation of spatial derivatives on an unstructured mesh (A.E. Dahoe) . . . . . . . . . . . 233
Instability of Transonic Flow over Airfoils at Singular Freestream Mach
Numbers (A.G. Kuz’min) . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Stochastic Flutter of Elastic and Viscoelastic Plates in a Supersonic Flow
(V.D. Potapov) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Fast numerical computing for a family of smooth trajectories in fluids flow
(G. Argentini) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
Hypersonic boundary-layer separation on a cold surface. (M. Kerimbekov) . 236
Contributed presentations (theme: Electronic industry) . . . . . . . . . . . 237
Simulation of Piezoelectric Materials: Iterative Solution Approaches for the
Forward Problem in Parameter Identification (M. Mohr) . . . . . . . . . . 237
Stochastic DAEs in Transient Noise Simulation (R. Winkler) . . . . . . . . . 238
Heavy traffic approximation for retrial queues with breakdowns (A. Aissani) 238
A Geometrical Approach to Quantum Holonomic Computing Algorithms
(K. Prykarpatsky) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
The Hodge theory of multidimensional Delsarte transmutation differential
operators and its application for integrable nonlinear dynamical systems
(K. Prykarpatsky) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Single-Phase AC to DC Converter with Active Power Factor Correction (A.
Maamoun) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240
Contributed presentations (theme: Life sciences) . . . . . . . . . . . . . . . 241
Mathematical models for long-term dosage of anticoagulant drugs (J. Cromme)241
Stochastic modelling and simulation in medicine and pharmacy (A. Prodan) . 242
Equilibrium of Two Populations Subjected to Chemotaxis (A. Mancini) . . . 242
Iterative Algorithms Used by Positron Emission Tomography Scanners:
RAMLA and its Main Properties (A.R. De Pierro) . . . . . . . . . . . . . 243
Rivalling Optimal Control in Robot-Assisted Surgery (G. Schanzer) . . . . . 243
Pattern Formation in Calcium Induced Calcium Released Reaction (I. Mincheva)244
Contributed presentations (theme: Water flow) . . . . . . . . . . . . . . . . 244
Numerical schemes for degenerate parabolic equations (I.S. Pop) . . . . . . 244
The flow and solidification of a thin liquid film on an arbitrary shaped substrate (T.G. Myers) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245
H5
H 11
H4
H 13
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Friday Afternoon
Electrolyte flow and temperature calculations in finite cylinder caused by
alternating current (A. Buikis) . . . . . . . . . . . . . . . . . . . . . . . .
Adaptive modeling in hydrodynamics (S. Perotto) . . . . . . . . . . . . . .
Multidimensional coupling in hydrodynamics (E. Miglio) . . . . . . . . . .
Animating Water Waves Using Semi-Lagrangian Techniques (M. El-Amrani)
16:15–16:45
246
246
247
247
Wacker lecture
Eigenvalue Problems in Periodic Surface Acoustic Wave Filter Simulations
(S. Zaglmayr) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248
The MEGAFLOW Project: Numerical Flow Simulation of Complete
Transport Aircraft
C. Rossow (DLR), N. Kroll, D. Schwamborn
Computational Fluid Dynamics (CFD) has become a central part of aerodynamic design for future aircraft. In anticipation of this role, during the last
decade in Europe and the US substantial research efforts were focussed on
the development of suitable numerical methods. MEGAFLOW represents an
initiative of the German aerospace research establishment DLR, industry, and
universities in Germany towards software development for sustained aeronautical application. The major goal of MEGAFLOW was to create a software
system which should:
a) allow 3D Navier-Stokes computations for complex configurations at
cruise and high-lift conditions,
b) establish numerical flow simulation as an essential and routinely used
tool at DLR and German aircraft industry.
The main approach was to concentrate and consolidate existing structured
flow solvers, and to develop an unstructured capability as an alternative. The
most relevant aspects of the initiative were to establish a single software platform for research and industrial application. For specific tasks, strategic cooperation with software vendors was sought. The validation of the software
system was always based on applications relevant for industry, and links to
other disciplines for multidisciplinary applications were established.
The MEGAFLOW software consists basically of two components, namely
the structured code FLOWer and mesh generator MegaCads, and the unstructured code TAU, which is primarily used in combination with the commercial
mesh generator CENTAUR of CentaurSoft.
BZ
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In the presentation, an overview with respect to organization and links to
other German and European projects will be given. The main components
with selected applications will be outlined, and a perspective of present and
future activities will be shown.
Minisymposium: Mathematical Tools of Signal Analysis in a Context of
Increasing Complexity.
F. Nekka (Université de Montreal), A.H. Siddiqi (King Fahd University)
Complex structures and phenomena pose a huge challenge when dealing with
their characteristic properties or their reconstruction processes. This minisymposium revisits some classical mathematical notions used in image analysis of scaling phenomena and proposes alternative parameters and methods to overcome the shortcomings of the classic ones. New fractal methods
will be presented. Illustration of these methods on signals exhibiting scaling
behaviour, including porous media, meteorology, astrophysics and genomic
data, will be shown.
Classification of Multiplicative Cascades: The Need to Modify the Usual
Autocorrelation Function.
L. Li (Université de Montreal)
This is the first time that the autocorrelation function approach is used in a
fractal context. We show how the classical autocorrelation concept can be
improved to be applicable in fractal analysis. This generalization is necessary
due to the degeneracy of the classical autocorrelation form proved for fractaltype distributed signals. We illustrate this fact on some known multiplicative
cascades. This work is in collaboration with Professor Fahima Nekka.
New Strategies for Texture Analysis of Different Complexity Degrees.
F. Nekka (Université de Montreal)
We give a general picture of our recent research in the context of texture
analysis, porous media in particular. We propose new strategies to deal with
different structures according to their degree of complexity. We show on
particular examples how the methods we developed can characterize texture
beyond the usual porosity and fractal dimension. This work is in collaboration
with Dr. Jun Li.
224
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Multi-fractal Analysis of Indian Rainfall Data
A.H. Siddiqi (King Fahd University of Petroleum & Mining)
Many real world phenomena such as climatic changes, turbulence, stock market to cite a few, are modeled using time series. Till recently statistical and
Fourier-based methods were extensively used to analyze time-series in order to detect long time trends, times of abrupt changes and seasonality and
for compression and denoising as well. However nowadays, wavelets and
wavelet-based multi-fractal formalism are becoming quite popular throughout developed and developing countries for studying many real world problems. In this study we illustrate the power of these new techniques in studying climatic data by analyzing the Indian rainfall recorded between 1813 and
1995 by wavelet-based multi-fractal formalism. This is a joint work with Dr.
Faouzi Khene.
Minisymposium: Wavelets and its Applications II
A.S. Tijsseling (Technische Universiteit Eindhoven), H.G. ter Morsche
(Technische Universiteit Eindhoven)
Friday, 14:15–16:15, Hall 7
Nowadays, wavelets (including the second generation wavelets) are used in a
broad spectrum of application areas like feature detection in images and signals, statistical analysis of time-dependent data, and computational methods
to solve partial differential equations, especially Boundary Element Methods
(BEM). The minisymposium Wavelets and its Applications (II) will address
the practically important area of leak detection in underground pipe systems.
Wavelet application for leak detection in water distribution systems
A.R. Simpson (University of Adelaide), M.F. Lambert (University of Adelaide), A.S. Tijsseling (Technische Universiteit Eindhoven)
Friday, 14:15–14:45, Hall 7
Wavelets have previously been applied to leak detection problems by several research groups. A discrete wavelet transform was used to identify leaks
based on a pressure trace during a transient event. The wavelet transform
involves a time convolution of the data trace with localised mathematical
functions and was designed to highlight discontinuities within the data trace.
These localised mathematical functions can be dilated or contracted in time
to produce the time convolution result at different scales and allow for the detection of small disturbances within the signal. The wavelet transform is best
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suited for the detection of discontinuities within the data trace, and is affected
in this situation by the shape of the injected transient, and also the rate of
sampling. The detection of a leak reflection at small scales will increasingly
become difficult as the shape of the injected transient signal deviates from a
perfect step/impulse. This is illustrated in the resultant wavelet coefficients
in previously published works, where the wavelet decomposition of the transient traces presented did not look particularly different between the leak and
no-leak cases. Problems in the application of wavelets to leak detection arose
due to (1) inaccuracy in wave speed estimation; (2) noise, which limits the
input shape and creates difficulty in identifying the singularity caused by the
leak; and (3) frequency dependent wave speed (dispersion) that added to uncertainty in the determination of the leak location. All of these issues lead
to uncertainty in leak location. This presentation will provide an overview of
previous work in using wavelets for leak detection and will describe a proposed research program to develop further new methods for using wavelets
and a proposed testing program (laboratory based and field testing).
Wavelet analysis of transients in pressurized pipes and leak detection
M. Ferrante (University of Perugia), B. Brunone (University of Perugia),
S. Meniconi (University of Perugia)
Friday, 14:45–15:15, Hall 7
Leak detection is a main issue in water resources management. The increasing demand for water prompts reconsideration of the management and supply of pipe systems. Difficulties in new water bodies exploitation can be
overcome by reducing water losses. Moreover, the current awareness in environment protection and water quality related issues fosters an increasing
interest in leak detection. There is a strong urge for methodologies for leak
detection and location that are quick and require less costly instrumentation.
They should not cause the cessation of pipeline operation, and not require that
the whole network be surveyed by trained personnel; leak detection methodologies based on transient analysis can achieve these goals. The time-history
of the pressure acquired during a transient at one or more measurement sections can be analyzed in the time domain and the location of the leak can be
determined by measuring the period of time which the pressure wave takes to
travel from the measurement section to the leak and vice versa. The pressure
waves arrival times correspond to sharp variations in the pressure time history that can be pointed out by the wavelet transform, retaining information
coming from the time domain analysis about leak position and size. In this
paper the analysis of transients in pipe systems is performed, by means of the
wavelet transform applied to numerical tests, and laboratory and field data.
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Such data consist of pressure signals related to transients in pressurized pipe
systems, with and without a leak. It is shown that wavelets can be used to locate leaks in the considered pipe systems as well as to capture main features
of transients.
Cross correlation, Wavelet and Cepstrum analyses for identifying reflection points in pipeline networks.
S.B.M. Beck (University of Sheffield), W.J. Staszewski (University of
Sheffield)
Friday, 15:15–15:45, Hall 7
It is well known that discontinuities in pipe networks give reflections to pressure waves that can be analysed to find the time delay between the original
signal and the reflected one. A leak in a pipe will also give a reflection point,
though possibly a more diffuse one. It is a reasonably straightforward task
(using, say, a cross correlation) to measure the time delay of the first reflection, but more complicated methods are required to extract data about further
reflections from - for example - the end of the pipe which has a leak in it.
This paper will describe the various methods that have been employed by the
Sheffield group to analyse the pressure traces due to water hammer pressure
pulses in pipe networks. These were conducted on both real (experimental)
and modelled networks. These started off using cross correlation techniques
with the refinement that additional reflections could be measured using the
change in gradient of the cross correlation. Then the orthogonal wavelet was
used to decompose the wave and a simple program was used to find the common periods in the higher order wavelet. Then Cepstrum techniques were
used to find the common pipe lengths in the network. Latterly, this has been
used in conjunction with wavelet analysis to filter the data. Finally, continuous wavelets are being used. These help to explain many of the results that
have previously been produced.
Overview of Leak Detection Methods and Application in the Field
H. Ramos (Instituto Superior Tecnico), D. Covas (Instituto Superior Tecnico), A. Young (Network Div. Scottish Water)
Friday, 15:45–16:15, Hall 7
A general overview of existing methods to detect and locate leaks in pipe systems is given. Field tests have been carried out in a Scottish Water real-life
system - the Lintrathen East Trunk main network (Dundee, UK) - with simulated pipe bursts. The collected transient data obtained in the field programme
have been used for testing and validating a number of novel transient-based
methodologies. This study was developed under Work Package 3 (WP3 -
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Leakage Detection) of the joint European Commission’s Fifth Framework
‘Growth’ Programme via the Thematic Network ‘Surge-Net’. The main objective of WP3 is leak detection in pipelines using transient pressure signals,
as well as the discussion about, and driving forward of, research on best practice in pipeline design software coding.
Minisymposium: Modelling and simulation of industrial filtration and
infiltration processes II
O. Iliev (Fraunhofer ITWM), C. Koenders (School of Math. Kingston
Univ.), A. Latz (Fraunhofer ITWM)
Friday, 14:15–15:15, Hall 14
Modelling and simulation of filtration and of infiltration are essential for
optimizing a variety of industrial processes and environmental applications.
These include processes in the automotive industry, food industry, chemical
industry, waste water treatment, etc. Filtration and infiltration processes are
characterized by a wide range of space and time scales (from nanometers
to meters, from nanoseconds to days), and by a strongly coupled interaction of different forces and phenomena (free flow and flow in porous media,
species and/or particles transport, electrical forces, chemical reactions, biological processes, etc.)
Present minisymposium will emphasize on the multiscale aspects, as well
as on the treatment of strongly coupled processes. Models and algorithms
for microscale (pore scale) and for macroscale filtration and infiltration processes will be discussed, together with certain upscaling strategies. Furthermore, coupling of flow of the free fluid with the flow in the porous media,
coupling of flow with particles transport and adsorption, influence of time
dependent forces on filtration, etc., will be presented and discussed. Special attention will be paid to discussing efficient numerical methods for the
considered problems. Specific features of models and algorithms, associated
with industrial filtration and infiltration processes will be outlined. The simulation and analysis of a number of industrial processes will be presented
and discussed in detail, demonstrating how mathematical modelling assists in
optimizing these processes.
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On efficient simulation of 3D flows of liquids through industrial filters
O. Iliev (Fraunhofer ITWM), V. Laptev (Fraunhofer ITWM), D. Vasileva
(Inst. Mathematics, BAS,)
Friday, 14:15–14:45, Hall 14
Flows through industrial filters are characterized by the needs of coupling
flow in the pure liquid regions with flow through porous media, by different
geometrical scales (e.g., filtering medium, such as fleeces and membranes, is
very thin for a large class of filters), etc. In certain cases the filter housing can
have a very complicated shape with different fine scale details (e.g., ribs in the
case of oil filters). In the case of numerical simulations, all these factors lead
to the necessity of using very fine (globally or locally) grids, with millions of
cells (elements).
3-D Navier-Stokes equations are used here to model the flow in the pure
liquid zones, and Brinkman equations are used to model the flow through the
filtering medium. Special attention is paid to developing an efficient algorithm for solving the coupled system of equations. This is a SIMPLE-type
algorithm, with a careful treatment of the Darcy term in Brinkman equation.
The algorithm is especially oriented to solving problems with very low permeability of the filtering medium, or with large viscosity of the filtrated fluid.
A software tool, SuFiS, based on the above described model and algorithm, is
developed. It performs simulation of 3-D flows through filters. The geometry
of the last is provided in a CAD format. Proper pre- and post-processing tools
complete SuFiS. SuFiS is validated in solving benchmark problems, as well
as in comparison with measurements carried out for several oil filters. Furthermore, our industrial partners use SuFiS for optimizing the design of oil
filters. Results from validations and from simulations for several industrial
filters are demonstrated.
Mathematical Modelling Of Flow Through Pleated Cartridge Filters
V. Nassehi (Loughborough University), W.R. Ruziwa (Loughborough University), A.N. Waghode (Loughborough University), R.J. Wakeman
(Loughborough University)
Friday, 14:45–15:15, Hall 14
Mathematical modelling of creeping incompressible Stokes flow and low permeability Darcy flow are well established and a number of reliable schemes
for the simulation of these regimes are available in the published literature.
However, modelling of combined Stokes/Darcy regimes, such as those encountered in many types of industrial filters, still presents mathematical and
practical challenges. In this paper we present a finite element model for the
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prediction and quantitative analyses of the hydrodynamic behaviour of deadend pleated cartridge filters. Elemental discretisation in this scheme is based
on using unequal order approximation functions for velocity and pressure
fields. We show that the used discretisation is able to generate unified stabilization for both Stokes and Darcy equations, avoid ‘numerical locking’
and preserve geometrical flexibility of the computational grid. Conducting
a number of numerical tests, it is shown that the developed model is capable of yielding theoretically expected and accurate simulations for realistic
industrially relevant problems. The model is tested for both Newtonian and
shear thickening non-Newtonian fluids which represent types of fluids used in
aeronautical applications. It has been demonstrated that the developed model
presents a cost effective, robust and reliable design tool to enable engineers
to appraise the operation of dead-end pleated cartridge filters.
Minisymposium: Net Campus for Modelling Education and Industrial
Mathematics
M. Heiliö (Lappeenranta Universtity of Technology)
Friday, 14:15–16:15, Hall 12
Ingenious exploitation of modelling and system technologies are means to
achieve competitive edge. Mathematics is becoming a generic ingredient in
innovative technology platforms in the European knowledge intensive industries. Virtual technologies and digital educational environments are a viable
media to support innovative processes. They can be used to bring solutions to
training and educational needs, to facilitate distributed and concurrent planning and consultation processes, provide remote access to software libraries
and knowledge repositories.
We discuss the challenge of using web based solutions in organising education in modelling and applied mathematics. We envisage the possibility
of building a European platform of educational services, a menu of courses
built on the concepts of current e-learning technologies, flexible access to
scientific software in modeling, numerical methods and scientific computing.
The lectures describe examples of web based courses in applied mathematics,
technologies for web publication of interactive documents and plans towards
international collaboration.
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Web Based Education of Mathematical Modelling - A Case Report.
S.A. Pohjolainen (Tampere University of Technology), E. Turunen (Tampere University of Technology), K Suomela (Tampere University of
Technology)
Friday, 14:15–14:35, Hall 12
As a part of the activities of the Finnish Virtual University the Department of
Mathematics at Tampere University of Technology is coordinating a national
network project on mathematical modelling. The purpose of the project is
to develop Web-based learning and teaching methods in mathematical modelling, to support content production and to develop the administrative measures needed to support web-based learning and teaching. Ten universities
and research institutes participate in the project and the teachers of the universities are responsible for teaching certain parts of the courses and for producing the corresponding courseware. Students from different universities
can study mathematical modelling both individually and collaboratively. In
this paper experiences obtained from course planning, courseware production, pedagogy, didactics, technology and student feedback will be presented
and analysed.
E-Learning Simulation: Creation and Delivery of Interactive Learning
Object in the Mathematical and Physics Didactical Domain
G. Iovane (University of Salerno), G.A. Gaeta (Matteo), S.A. Salerno
(Saverio)
Friday, 14:35–14:55, Hall 12
We present in this paper an innovative e-learning platform which integrates
some techniques coming from different research areas such as Artificial Intelligence, Information Retrieval and Semantic Web. The aim of the platform is
to provide a flexible e-learning instrument able to support learners during the
whole training cycle, from the definition of the objectives to the assessment
of the results, through the construction of custom self-adaptive courses. IWT
aims to fill some lacks of the present e-learning systems, such as: 1) The common e-learning systems usually do not allow the customisation of the courses
on the student profile but simply propose standard courses; 2) They usually
limit themselves to deliver learning material to the student, without trying to
interact with him through a model of her/ his mind; 3) They usually exploit
possible test results only for checking the student’s acquired knowledge level
but do not use such a knowledge also for changing the quantity and quality
of the delivered learning material itself; 4) They do not take into account the
student’s preferred learning styles. Moreover, in this work we show our approach for using IWT to build interactive Learning Object (LO) in the physics
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and mathematics field. Our experience in the e-learning application, suggests,
that in order to produce LO of good quality, related to a particular didactical
domain, it need translate the instruments and standards of the domain in the
new e-learning environment. IWT is a system to follows this thinking, so,
it furnishes the special Drivers and Plug-Ins components by specializing the
generic platform in the domain platform. The LO creation process merges the
conventional procedure for the description of the mathematical model, with a
new technique to introduce into the LO specifics didactical information.
A web supported Applied Mathematics course
G. Faraco (Universita della Calabria), P. Pantano (Universita della Calabria), F. Stranges (Universita della Calabria)
Friday, 14:55–15:15, Hall 12
The on-line course of Applied Mathematics available at http://galileo.
cincom.unical.it/corsi/Newmetodi/ing_meccanica/index.
html of the University of Calabria proposes, in a new way, topics as nonlinear dynamic systems, chaos theory and fractals highlighting teaching on-line
and use of simulations. The aim is to create a learning environment which allows one the exploration of the main characteristics of these new paradigma
of science through computational models. The on-line course allows teachers
and students to interact at distance surfing in hypermedial materials (texts,
graphics, software, video, audio, etc.) in both a synchronous and an asynchronous way. The on-line corse was experimented with the students enrolled in the Applied Mathematics course of the programme for a degree in
Mechanics Engineering. The students have been invited to use, as support
to theoretical lessons, the material available in the web site (lessons in pdf
format, exercises connected to the topics of the theoretical lessons, exercises
with solutions, structuralized tests, questionnaries, source codes in software
programme and demo). An appropriate questionnaire has tested the usability
of the web site as regards the contents, the graphical interface and the technical functionalities. In this work we present the results of the experimentation.
An Integrated Framework for Web Publication of Interactive Documents
A.M. Anile (University of Catania), G. Grasso (University of Messina)
Friday, 15:15–15:35, Hall 12
In this work a framework is described in which a LATEX document, together
with some simulations, can be easily translated into an interactive WWWbased document. The process consists of three steps: 1) the addition of few
LATEX tags to the original document; 2) the translation of LATEX sources into
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HTML, including pictures, graphs and formulas; 3) the automatic creation
of navigation links defining different paths through the same document and
links to external programs. Also the interactive links are generated on the
basis of the initial content of the LATEX document through the use of purpose
written macros. This last point is crucial as with few lines of LATEX code a
gateway can be produced inside the document that calls any external program
which takes parameters from the interactive document and generates numeric,
graphical or animated output. Examples af application of this methodology
in the creation of lecture courses on Dynamical Systems and Electric Circuit
Simulation are given.
Towards a European Net Campus for Industrial Mathematics
M. Heiliö (Lappeenranta Universtity of Technology)
Friday, 15:35–15:55, Hall 12
The cutting edge knowledge in mathematical technology in Europe is found
dispersed at relatively small nodes of excellence. The use of virtual technologies and digital educational environments could help to exploit this expertise
and knowledge pool. We present an initiative to build a European digital
environment and service-grid structure for applied mathematics. The aim is
a flexible integrated e-work environment for training, learning and research
tasks. It would support complex problem solving in science, society, industry
and businesses. The features of the proposed project :
Netcampus of educational services, courses built on the current eLearning technologies. Access to a library of software in modelling, numerical
methods and scientific computing. Feasibility and pilot study on the business model of content production Research on forefront technology in webpublishing
Interested universities are sought. Each partner institute would be committed to develop and produce 1-3 course environments, based on local strengths.
Some of the course topics may be tailor-made for a special industry, based on
demand in R&D and needs in educating industrial mathematicians or research
scientists. Those interested in the plan are encouraged to bring further ideas
to the discussion.
A system for distance graduate studies and scientific cooperation in the
Internet environment; development and applications
J. Mockus (State Research Institute of Mathematics and Informatics, Vilnius)
Friday, 15:55–16:15, Hall 12
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This paper deals with development of Web-based integrated system for distance graduate studies and scientific cooperation . A number of economical,
financial and social models are considered as examples of the theories of optimization and games. The system is aimed to support core curriculum and
to provide students with hand-on experience on effective use of open-source
software tools. The main objective is too stimulate and develop creative abilities to work as independent researchers. This is achieved by putting together
the general theories and a number of examples developed by students themselves. New students improve existing examples or develop some new ones.
Most examples are in implemented in Java. That makes distance studies simple and convenient. However other languages are used as well, for comparison. The main web-site is http://soften.ktu.lt/˜mockus There
are several mirrors, too.
Contributed presentations (theme: Aerospace)
Application of visco-plastic behavior of composites - bounds on overall
properties
P. Procházka (CTU Prague, Civil Engineering)
Friday, 14:15–14:35, Hall 5
This problem is solved by the technique known from Hashin-Shtrikman variational principles. The boundary element method is the numerical tool. A
mathematically correct formulation will be established, and the boundary element formulation will follow. Cylindrical structures will be assessed by the
above-mentioned technique. Optimal design leading to optimal bearing capacity will be discussed. The optimization and visco-plastic behavior will
be involved in eigenparameters (eigenstresses or eigenstrains). The eigenparameters can express prestressing, visco-plastic behavior or other phenomena
from the field of hereditary problems and others. The idea starts with TFA
(transformation field analysis) by Dvorak, RPI, USA, which was generalized
by the same author and author of submitted abstract to general composite
structures. The former publication on this topic was concerned with linear
problems. Results from studies on hollow cylinders will be presented to show
the ability of the method.
On the application of least-squares reconstruction in the computation of
spatial derivatives on an unstructured mesh
A.E. Dahoe (Technische Universiteit Eindhoven), L.P.H. de Goey (Technische Universiteit Eindhoven), R.S. Cant (University of Cambridge)
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Friday, 14:35–14:55, Hall 5
The potential of a methodology to remedy the occurrence of high frequency
oscillations in the spatial derivatives computed on an unstructured tetrahedral
mesh was explored. To verify our methodology, called Least-Squares Gradient Reconstruction, the diffusion equation was solved as a test-case for the
problem of an instantaneous spherical surface source enclosed by a spherical
domain. The same problem was also solved by means of the Finite Volume
Method based on the Green-Gauss theorem for the sake of comparison. The
origin of these high frequency oscillations could be identified by analyzing
the application of the Green-Gauss theorem on an unstructured mesh. Based
on the same arguments it was anticipated that Least-Squares Gradient Reconstruction would constitute a remedy to the problem. This expectation was
confirmed by numerical simulations. It was also anticipated that combining the Green-Gauss theorem with a reconstruction of the average value at
a cell-face in the least-squares sense would mitigate or remedy the problem.
Numerical simulations indicate that the contrary appears to be the case.
Instability of Transonic Flow over Airfoils at Singular Freestream Mach
Numbers
A.G. Kuz’min (St. Petersburg State University)
Friday, 14:55–15:15, Hall 5
We address airfoils with a minimum of the curvature in the midchord region.
The minimum may cause formation of a few supersonic regions adjacent to
the upper and lower surfaces of the airfoil. The supersonic regions typically
amalgamate when the freestream Mach number M∞ increases, and they split
into smaller ones when M∞ reduces. Recent numerical simulations based on
the Euler equations and a high-resolution numerical technique have demonstrated that the splitting/amalgamation of the local supersonic regions proceeds in a discontinuous manner [1, 2]. Hence, there exist singular values
Ms of the Mach number M∞ which trigger off the restructuring of the steady
flow. Consequently, at M∞ = Ms , the inviscid transonic flow is unstable
with respect to perturbation of the boundary conditions. This phenomenon
was studied in [1, 2] for flow in a channel of variable cross section.
In this work, the structural instability of steady transonic flow at singular Mach numbers is analyzed for symmetric airfoils and the nonsymmetric
DSMA523 and Whitcomb configurations. A discontinuous dependence of
the lift coefficient C L on the angle of attack and M∞ is demonstrated. The
physical nature of the instability is discussed.
The restructuring of the flow at M∞ = Ms accounts for the great sensitivity of transonic flow to changes in boundary conditions studied in a number
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of papers. Also, an analysis of the instability contributes to the understanding of the nonunique transonic solutions which occur at certain freestream
conditions.
[1] Kuz’min A.G. Interaction of a shock wave with the sonic line. IUTAM Symposium Transsonicum IV. Kluwer Academic Publishers. 2003, 13–18.
[2] Ivanova A.V. The structural instability of inviscid transonic flow in a channel. J.
of Engineering Physics and Thermophysics. 2003. Vol. 76, no. 6, 58–64.
Stochastic Flutter of Elastic and Viscoelastic Plates in a Supersonic Flow
V.D. Potapov (Moscow State University of Means Communi)
Friday, 15:15–15:35, Hall 5
The stability of an elastic or viscoelastic plate in a supersonic flow, moved
with a constant speed, is investigated. The plate has an initial random curvature. An uniform load is applied in the level of the middle flatness and
suggested as a wide-band random stationary process. Using the piston theory, nonlinear equations of the plate motion are written for the case of linear
constitutive relations and finite deflections. With help of Bubnov-Galerkin
method these equations are reduced to systems of ordinary integro-differential
equations. The stability is considered in Lyapunov sense and with this purpose the system of linearized integro-differential equations in perturbations
is used. For the simulation of random realizations of wide-band stationary process, corresponding to the variation of the load in time, a numerical
procedure, based on the method of canonical expansion, is employed. For
each realization of the load and of the initial curvature the numerical solution of the system of integro-differential equations, describing the dynamic
nonperturbed and perturbed behavior of the plate, is found. With the help
of Liapunov exponents, which are calculated for the solution of linearized
equations, the conclusion about the stability of the nonperturbed motion of
the plate can be made. For a large enough sample of similar solutions the
probability of the stability or instability of the plate is obtained. The similar
approach is used for the investigation of the stability with respect to statistical moments of the searched unknown functions of linearized equations. The
influence of probabilistic characteristics of random processes, of the random
initial curvature, of viscous characteristics of the material and flow speed on
the stability of the plate is studied.
Fast numerical computing for a family of smooth trajectories in fluids
flow
G. Argentini (RIELLO GROUP)
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Friday, 15:35–15:55, Hall 5
In this work I present a technique of construction and fast evaluation for a
family of cubic polynomials for analytic smoothing and graphical rendering
of particles trajectories for flows in a generic geometry. The principal aims
of the work are: 1. an improved technique to obtain smoothed geometric
lines even in situations where there are few data-points or where the flow is
turbulent; 2. a fast and efficient evaluation of these polynomials in a large
set of values for a good resolution of graphic rendering; 3. the measure of
speedup and efficiency for scientific and technical applications using cluster
computing techniques. The numerical approch is based on a cellular automaton evolving on a three-dimensional grid. The smoothed curves are then computed by interpolation of data-points using a combination of Bézier method
and piecewise cubic splines, and imposing adequate conditions for slope and
curvature. The functions so computed have regular properties and avoid the
possible rising of spurious wiggles and other not realistic effects as Gibbs
phenomenon. For an appropriate visualization of the flow, we use a computational method based on an appropriate distribution of the polynomials among
the available processors. The efficiency of the used method is good, mainly
reducing the number of floating-points computations by caching the numerical values of the polinomials parameter’s powers, and reducing the necessity
of communication among processes. The computation is performed using a
customized parallel environment for the package Matlab on a multiprocessor
cluster. The work permits to deduce these conclusions: a. it is possible to
obtain smooth and realistic rendering of a flow even in generic geometry; b.
the parallel method used has a good speedup (0.8-0.9). This work has been
developed for the Research & Development Department of our company for
planning advanced customized models of combustion chambers.
Hypersonic boundary-layer separation on a cold surface.
M. Kerimbekov (University of Manchester)
Friday, 15:55–16:15, Hall 5
An asymptotic theory of laminar hypersonic boundary-layer separation for
large Reynolds number has been described for situations when the surface
temperature is small compared with the stagnation temperature of the oncoming gas flow. The interactive boundary-layer structure near separation is
described by well-known triple-deck concepts but, in contrast to the classical
case, wall cooling leads to a decrease in displacement thickness of the viscous sublayer. The contribution to the displacement due to the main part of
the boundary layer 1δ is proportional to the induced pressure rise according
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to
1δ = L p,
Z
where
L=
0
δ
1
−
1
dy
M 2 (y)
is the Pearson’s integral.
Here δ denotes the boundary layer thickness and M(y) is the Mach number
distribution across the boundary layer. If the average Mach number is less
than unity, L > 0 and a pressure increase leads to boundary-layer thickening,
as in the case of a subsonic flow. On the other hand if L < 0, a pressure rise
produces a decrease in boundary-layer thickness as is usual for supersonic
flows. Consequently, a boundary layer with L > 0 is referred to as subcritical
and that with L < 0 is termed as supercritical.
An interesting possibility arises when the oncoming boundary layer has
L = 0, this case has been referred to as transcritical. The flow in the viscous
sublayer is governed by the classical boundary-layer equations with the prescribed pressure gradient, and the solution has a singularity at the separation
point. A main objective of this work is to show how the singularity may be
removed in the framework of marginal separation theory.
Contributed presentations (theme: Electronic industry)
Simulation of Piezoelectric Materials: Iterative Solution Approaches for
the Forward Problem in Parameter Identification
M. Mohr (University of Erlangen)
Friday, 14:15–14:35, Hall 11
One of the fields of engineering science in which numerical simulation and
especially the identification of material parameters is playing a role of increasing importance is the design of piezoelectric transducers. In this application the sought-after parameters are the elastic stiffness constants, dielectric
constants and piezoelectric constants that describe the electrical and mechanical behaviour of piezoelectric ceramics and their coupling. These parameters
form the coefficient tensors in a system of PDEs. Thus, the identification
problem consists in identifying these tensors.
In order to determine the parameters and solve this inverse problems the
corresponding forward problem, i.e. the determination of the material behaviour for assumed parameters must repeatedly be solved numerically. A
performant identification algorithm therefore requires efficient methods for
this evaluation sub-task. This holds even more since in realistic simulations
the non-linear and time-dependent behaviour must be taken into account.
Since the finite element discretisation of the piezoelectric PDEs results in a
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symmetric but indefinite linear system of equations, appropriate solvers have
to be developed for this class of problems.
In this talk we present different preconditioners and Krylov subspace methods that were adapted to the special structure of the forward problem and
highlight their drawbacks and advantages. These results will be verified by
selected numerical studies.
Stochastic DAEs in Transient Noise Simulation
R. Winkler (Humboldt-University Berlin)
Friday, 14:35–14:55, Hall 11
The increasing scale of integration, high tact frequencies and low supply voltages cause smaller signal-to-noise-ratios. In several applications linear noise
analysis is no longer satisfactory and thus transient noise analysis becomes
necessary.
We deal with the thermal noise of resistors as well as the shot noise of semiconductors modeled by additional sources of additive or multiplicative white
noise currents. The resulting system is described by a stochastic differential
algebraic equation (SDAE) of the form
Z t
Z t
A(X (t) − X (t0 )) +
f (X (s), s)ds +
G(X (s), s)d W (s) = 0 ,
t0
t0
where A is a constant singular matrix which is determined by the topology
of the electrical network and W is a k-dimensional Wiener process. One
has to deal with a large number of equations as well as of noise sources.
Using techniques from the theory of DAEs as well as of the theory of SDEs
we derive existence and uniqueness for the solutions as well as convergence
results for certain implicit methods for systems with DAE-index 1. In general
their order of convergence is only 1/2. Nevertheless we discuss the potential
of methods with deterministic order 1 and 2 for systems with small noise.
For the drift-implicit Euler scheme we present a stepsize-control that is based
on the mean square of local error estimates. For illustration we apply the
drift-implicit Euler scheme with stepsize control to an oscillator circuit.
Heavy traffic approximation for retrial queues with breakdowns
A. Aissani (University of Science & Technology USTHB)
Friday, 14:55–15:15, Hall 11
We consider an MX/G/1 retrial queueing system where customers arrive according to a compound Poisson process with random arrival size. The server
is subject to three types of interruptions. The “vacation” interruptions are
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239
usually planned in advance in order to exploit idle time of the server. The
server is subject to both active (passive) breakdowns which may occurs when
the server is busy (idle) according to a Poisson process.
A customer who arrives and finds the server busy, on vacation or broken
down joins a retrial group (a sort of queue) and repeat his request according to
given retrial policy. The distribution functions of retrial times, service times
and vacation times are arbitrary distributed. Similar models have been used
in several studies devoted to performance assesment of Switching Networks,
Digital Cellular Mobile Networks, Local Area Networks under the protocols
of random multiple access, and so on
We use the generating function method to evaluate several performance
measures of interest, particularly, the influence of reliability upon these measures. Next, we show that the limiting distribution of the system state under
heavy traffic follows an exponential distribution. This gives simple approximating expressions for the computation of these measures.
A Geometrical Approach to Quantum Holonomic Computing Algorithms
K. Prykarpatsky (AMM), D. Blackmore (NJIT), N.K. Prykarpatska (AMM)
Friday, 15:15–15:35, Hall 11
A general approach to quantum holonomic computing based on geometric
Lie-algebraic structures on Grassmann manifolds and related with them Lax
type flows is proposed. Making use of the differential geometric techniques
like momentum mapping reduction, central extension and connection theory
on Stiefel bundles it is shown that the associated holonomy groups properly
realizing quantum computations can be effectively found concerning diverse
practical problems. Two examples demonstrating 2-form curvature calculations important for describing the corresponding holonomy Lie algebra are
presented in detail. Quantum Computer Algorithms like that above can effectively solve, as is well known UNITON, a lot of important for applications problems not solvable generally in a reasonable time by usual classical
computers. i) factorization of a large integer x ∈ Z+ by its primes (P. Shor,
1994) and application it to encrypting messages encoded via the RSA system;
ii) search or sorting algorithm for finding an item in structured and unstructured data sets (L.K. Grover, 1996; T. Hogg, 1997); iii) fast discrete Fourier
transform (P. Shor, 1994). Some examples which were recently treated by
means of the Quantum Computing Algorithms are discussed, in particular,
Holonomic Quantum Computations: a) Two-mode quantum-optical model,
b) Lax-type flows model QM : Prykarpatsky A.K. Quantum Mathematics
and its Applications. Part 1. Automatyka, AGH Publisher, Krakow, 2002,
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v.6, N1, p. 234-2412; Quantum Mathematics: Holonomic Computing Algorithms and Their Applications. Part 2. Automatyka, 2004, v.7, N1. UNITON
: Rieffel E. and Polak W.: An introduction to Quantum Computing for for
Non-Physicists, xxxlanl archive: quant-ph/9809016.
The Hodge theory of multidimensional Delsarte transmutation differential operators and its application for integrable nonlinear dynamical systems
K. Prykarpatsky (AMM), D. Blackmore (NJIT), Y.A. Prykarpatsky (BNL
SDIC and AMM of Krakow)
Friday, 15:35–15:55, Hall 11
The Hodge theory of multidimensional Delsarte-Darboux transmutation operators in parametric functional spaces is studied by means of differentialgeometric and topological tools. It is shown that kernels of the corresponding
integral operator expressions depend on the topological structure of related
homological cycles in the coordinate space. As a natural realization of the
construction presented we build pairs of Lax type commutative differential
operator expressions (see [1],[2],[4],[5]) related via a Delsarte-Darboux transformations [3] and having a lot of applications in spectral and soliton theories.
[1] Nizhnik L.P. Inverse scattering problems for hyperbolic equations. Kiev, Nauk.
Dumka Publ., 1991 (in Russian)
[2] Samoilenko A.M., Prykarpatsky Y.A. and Samoylenko V.G. The structure of
Darboux-type binary transformations and their applications in soliton theory.
Ukr. Mat. Zhurnal, 2003, v. 55, N12, p.1704-1723 (in Ukrainian)
[3] Matveev V.B. and Salle M.I. Darboux-Backlund transformations and applications. NY, Springer, 1993.
[4] Prykarpatsky A.K.., Samoilenko A.M. and Prykarpatsky Y.A. The multidimensional Delsarte transmutation operators, their differential-geometric structure and applications. Part.1. Opuscula Mathematica, 2003, v. 23, p.71-80
[5] Samoilenko A.M. and Prykarpatsky Y.A. Algebraic-analytic aspects of completely integrable dynamical systems and their perturbations. Kyiv, NAS, Inst.
Mathem. Publisher, 2002, v.41. (in Ukrainian)
Single-Phase AC to DC Converter with Active Power Factor Correction
A. Maamoun (Electronics Research Institute), A.M. Soliman (Electronics Research Institute), A.M. Kheireldin (Faculty of Eng,Ain Shams
Univ.)
Friday, 15:55–16:15, Hall 11
Single-phase rectifiers have been widely used in low-to-medium power applications. These conventional rectifiers suffer from high content of harmonics
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in supply currents and high output dc voltage ripple. The resulting input
power factor is also poor. The boost converter is one of the most popular
choices for high-quality rectification. The converter is supplied from a fullwave rectified line voltage and operated so that the input current follows the
input voltage. The input current shaping results in low line current harmonic
distortion and a power factor close to unity at the interface between the ac
line and the rectifier.
The clamped-current boost rectifier is used as the proposed model for
power factor correction (PFC) rectifier. Current-mode pulse width modulator is used to control the boost converter. The output dc voltage of the
converter is regulated by voltage regulation loop where an error amplifier is
used as a proportional-integral (PI) regulator. The output of the PI provides
the reference current for the current control loop. The parameter values of the
designed model can be selected so that a relatively low harmonic distortion,
low component stresses, and low inductive energy storage can be achieved
simultaneously.
The proposed model of high power factor boost rectifier is simulated for
a wide range of loads by using the Matlab software package. The supply
current waveforms, the supply current spectra and the output dc voltage are
given in the simulation results.The implementation of the proposed model
for single-phase PFC boost rectifier is introduced. The experimental results
verify the simulation results.The designed converter has been used as a DC
voltage source for PWM inverter feeding an induction motor.
Contributed presentations (theme: Life sciences)
Mathematical models for long-term dosage of anticoagulant drugs
J. Cromme (BTU Cottbus)
Friday, 14:15–14:35, Hall 4
Prescription of anticoagulant drugs for ‘blood-thinning’ is a widespread precaution for patients with high thrombosis risk like patients with an artificial
heart-valve. To achieve the target corridor for the concentration of the agent
in the patient’s blood, correct dosage of the orally taken drug is mandatory.
Expert systems may help to achieve better dosage recommendations. Mathematical models form an important component of such systems. On the one
hand such models should be simple and easy to implement, on the other hand
allow for all necessary adjustment to an individual patient’s time dependent
reaction. We present linear and nonlinear models based on stochastic parameters like a specific time-dependent ‘resorption factor’ and discuss their
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usefulness in predicting INR values as an important step towards a dosage
calculator.
Stochastic modelling and simulation in medicine and pharmacy
A. Prodan (Iuliu Hatieganu University), RC Remus Campean (Iuliu Hatieganu University), MR Madalina Rusu (Iuliu Hatieganu University)
Friday, 14:35–14:55, Hall 4
Previous research has shown the advantages of stochastic models for representation of real world activities, phenomena and processes. Based on
theoretical fundamentals in stochastic modelling and simulation, we implemented an incremental development of an object-oriented Java framework for
stochastic modelling, analysis and simulation of problems arising in a practical context, particularly in medicine and pharmacy. We used this framework
to create stochastic models, which accurately represent real world phenomena
and processes, particularly in health care, patient monitoring and pharmacy.
We modeled the flow of patients around departments of geriatric medicine. In
order to simulate the model, we have split it into two parts: the arrival of patients and the in-patient care. We modeled the arrival of patients as a Poisson
process with a parameter estimated by using the inter-arrival times. These
times are independent exponential random variables, each with a parameter λ
and with a corresponding density function. The care time is modeled by the
application of a mixed-exponential distribution, where the number of terms in
the mixture corresponds to the number of stages of patient care. A common
scenario is that there are two stages for in-patient care: acute and long-stay,
composing in this case two exponential distributions with some particular parameters, representing the corresponding access rate for each stage.
Based on the same Java framework, we implemented bootstrapping methods with the purpose of simulating laboratory works and experiments, in both
didactic and research activities. Using a bootstrapping tool, the experimenter
can repeat the original experiment without any consumption of substances
and reactants, obtaining pseudo-data as plausible as those obtained from the
original experiment. Our bootstrapping tools use the computer power to create pseudo-samples, to obtain reliable standard errors, confidence intervals
and other measures of uncertainty for a wide range of problems.
Equilibrium of Two Populations Subjected to Chemotaxis
A. Mancini (Universitá di Firenze), A. Fasano (Univ. di Firenze), M.
Primicerio (Université di Firenze)
Friday, 14:55–15:15, Hall 4
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We consider a system of four partial differential equations modelling the dynamics of two populations interacting via chemical agents. Classes of nontrivial equilibrium solutions are studied and a rescaled total biomass is shown
to play the role of a bifurcation parameter.
Iterative Algorithms Used by Positron Emission Tomography Scanners:
RAMLA and its Main Properties
A.R. De Pierro (State University of Campinas)
Friday, 15:15–15:35, Hall 4
The first time a Maximum Likelihood approach was suggested for Positron
Emission Tomography (PET) was in 1976, by Rockmore and Mackovski
(IEEE Trans. Nucl. Sci., 23, pp. 1428-1432). The EM algorithm, proposed
by Shepp and Vardi (IEEE Trans. Med. Imaging,1, 113-121, 1982) was for
many years the main option chosen by researchers to solve the corresponding
mathematical optimization problem. But it was only after more than a decade
that fast iterative methods like OS-EM by Hudson and Larkin (IEEE Trans.
Med. Imaging,13, 4, 601-609, 1994), and RAMLA by Browne and De Pierro
(IEEE Trans. Med. Imaging, 15, 4, 687-699, 1996 [1]) were adopted by PET
scanners (Siemens, GE, Phillips). In spite of their success, only a restricted
convergence analysis was presented in [1] and Bayesian regularization methods have not yet been incorporated. After a brief story about the introduction
of iterative methods in real scanners, in this article we present a full convergence proof for RAMLA, valid for its extension BSREM (De Pierro and
Yamagishi, IEEE Trans. Med. Imaging, 20, 4, 280-288, 2001) to the regularized problem. Also we analyze experimentally the behavior of the method
with respect to its main parameters: number of blocks (views, projections),
relaxation, number of iterations and bayesian regularization. We illustrate the
results using simulated tomographic data.
Rivalling Optimal Control in Robot-Assisted Surgery
G. Schanzer (Technische Universität München), R. Callies (Technische
Universitaet Muenchen)
Friday, 15:35–15:55, Hall 4
Robotic manipulators are a key element in future high-precision minimally invasive surgery and telesurgery. This development is supported by the rapidly
decreasing size of robotic sensors and actuators which allow the construction of miniaturized artificial fingers and hands of increasing complexity. The
driving of the micro-joints is one of the major current limitations for further
progress. Either actuators are fast, but produce only small specific forces (e.g.
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by piezo actuators), or high specific forces can be generated with a slow rate
of change (e.g. by shape memory alloys).
In our paper we investigate the optimal control of an advanced fivesectional branched manipulator consisting of two fingers with two joints each,
which are mounted on the same rotational base. Joints are driven with fast and
strong actuators connected in parallel. This leads to the new and challenging
problem of optimal control of multibody systems subject to rivalling controls
with specific constraints on the maximum and on the first derivative of the respective control. Several objective functions are investigated: Energy optimal
and mixed time-energy optimal motions are calculated and compared in order
to achieve human-like motions. The differential equations for the state and
adjoint variables are recursively defined to allow a fast and efficient treatment.
Geometric constraints induce state constraints of second order. The complete
problem of optimal control is transferred into a piecewise defined, highly nonlinear multi-point boundary value problem without any simplifications. The
numerical solution of the boundary value problem is by the advanced multiple
shooting method JANUS. Additional numerical difficulties arise from the difference between the fast and the slower dynamics of the respective controls;
these difficulties have been overcome in JANUS by split integration schemes.
Pattern Formation in Calcium Induced Calcium Released Reaction
I. Mincheva (Wilfrid Lauirier University)
Friday, 15:55–16:15, Hall 4
We consider calcium induced, calcium released chemical model for oscillations of calcium concentration in muscle cells. It is assumed that the law
of mass action applies. Then the reaction-diffusion system representing the
model consists of four equations. We apply a theory called Stoichiometric
Network Analysis (SNA) developed by B. Clarke and improved by A.N.
Ivanova. Necessary and sufficient conditions on the parameters of the system are derived for pattern formation. The necessary condition includes, the
ratio of some of the diffusion coefficients is larger than one.
Contributed presentations (theme: Water flow)
Numerical schemes for degenerate parabolic equations
I.S. Pop (Technische Universiteit Eindhoven)
Friday, 14:15–14:35, Hall 13
Many porous media processes are modelled by degenerate parabolic problems: gas or fluid flow, (in)filtration phenomena, reactive flow. A particular
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feature of such problems is the possible change of their parabolic character
into an elliptic or hyperbolic one, featuring slow or fast diffusion phenomena.
In this talk we present some regularization based discretization schemes,
which are analyzed numerically. Specifically, we demonstrate their convergence by rigorous estimates of the approximation error in terms of the discretization parameters.
The flow and solidification of a thin liquid film on an arbitrary shaped
substrate
T.G. Myers (University of Cape Town), J.P.F. Charpin (University of Cape
Town), S.J. Chapman (University of Oxford)
Friday, 14:35–14:55, Hall 13
The flow and solidification of a thin fluid film has applications in many natural
and industrial processes. Examples include ice accretion from a thin water
layer, spray forming and numerous coating processes. In this talk a model will
be developed for fluid flow and solidification on an arbitrary shaped threedimensional surface, where the surface is maintained below the solidification
temperature.
When solidification is neglected the model describes a standard lubrication
approximation for flow on an arbitrary surface. It will be shown how a number
of simpler flow models may be retrieved. The full model will then be reduced
to deal with flow and solidification on standard substrate shapes, such as a flat
surface, cylinder and sphere.
Numerical and analytical results will be presented for practical examples,
such as:
1) water flow on an initially dry surface, due to a localized incoming fluid
source (rain) and driven by gravity and air shear;
2) ice accretion on power lines and in-flight aircraft.
The work in this talk is described further in [1, 2]. The model also forms
part of a commercial aircraft icing code, ICECREMO, see [3] for example.
[1] Myers T.G., Charpin J.P.F. & Chapman S.J. The flow and solidification of a thin
fluid film on an arbitrary three-dimensional surface. Physics of Fluids 14(8)
pp2788-2803 2002.
[2] Myers T.G., Charpin J.P.F. & Thompson C.P. Slowly accreting glaze ice due
to supercooled droplets impacting on a cold substrate. Physics of Fluids 14(1)
pp240-256 2002.
[3] Moser R. & Gent R.W. Experience from application of a 3D
Ice
accretion
code.
http://icebox-esn.grc.nasa.gov/ext/documents/
sae/Inflight/FAAID14 Moser.pdf. FAA In-flight icing/ground de-icing international conference and exhibition, 2003. Paper no. 2003-01-2133.
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Electrolyte flow and temperature calculations in finite cylinder caused by
alternating current
A. Buikis (Institute of Mathematics), H. Kalis (Institute of Mathematics)
Friday, 14:55–15:15, Hall 13
One of the modern areas of application developed during last years is effective use of electric energy in production of heat energy. In our previous papers
the electrolyte flow and temperature calculations caused by two-phase current
with 6 circular electrodes was considered. Here we consider 9 circular electrodes with three-phase axially-symmetric system of alternating current with
phase shift 120 degrees and calculate the distribution of electromagnetic field
and forces, electrlyte flow and temperature in finite cylinder. We obtain the
magneto-hydrodynamic flow of viscous incompressible fluid and distribution
of temperature by a monotonous finite difference scheme. The numerical
results depend basically of the swirl number and of the arrangement of electrodes.
Adaptive modeling in hydrodynamics
S. Perotto (MOX - Politecnico di Milano), E.M. Miglio (MOX - Politecnico di Milano), F.S. Saleri (MOX - Politecnico di Milano)
Friday, 15:15–15:35, Hall 13
The study of free surface flows leads to consider a wide range of physical
phenomena, from tidal flows, to water motion in large basins, river courses,
channels, etc. Ideally, one should solve the full 3D Navier-Stokes equations
to capture all the physical features of the problem at hand. However, this
approach is characterized by a huge computational effort. In this talk we
will consider models of different physical nature (i.e. derived under different
physical assumptions). According to this physical classification hydrostatic
models (for instance, Boussinesq and Serre equations) are generally opposed
to the non-hydrostatic ones (the Saint-Venant equations).
The approach we are advocating consists in a suitable coupling of the above
mentioned models by solving the more expensive models only in the regions
of the domain where it is strictly necessary. The matter now is: how to identify the regions where the simpler and the more complex model has to be
solved, respectively.
A suitable a posteriori modeling error estimator can be used to detect the regions where each model can be conveniently employed. The coupling of different hydrodynamics models, driven by an a posteriori estimator, is tackled
in this talk. We move from the modeling error theory provided in by A. Ern
and M. Braack, where a dual problem, associated with the problem at hand,
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247
is solved in order to measure the influence of the model on a user-defined
output functional of the numerical solution. This approach is an extension
to modeling error analysis of the well-known dual-weighted residual method
provided by R. Becker and R. Rannacher for the a posteriori discretization
error control.
Finally some numerical results are provided to assess the effectiveness of
the proposed approach.
Multidimensional coupling in hydrodynamics
E. Miglio (MOX - Politecnico di Milano), S.P. Perotto (MOX Politecnico
di Milano), F.S. Saleri (MOX Politecnico di Milano)
Friday, 15:35–15:55, Hall 13
The study of free surface flow leads to consider a wide range of physical
phenomena, from tidal flows, to water motion in large basins, river courses,
channels, etc. With the aim of reducing the computational cost, a hierarchy
of hydrodynamic simplified models have been proposed in the literature. In
this talk we will deal with models of different dimension. According to dimensional classification, for the 3D case we can consider the free surface
Navier-Stokes or the hydrostatic 3D shallow water equations; concerning the
2D situations the Boussinesq, Serre or Saint-Venant equations can be adopted;
finally the 1D counterpart of these latter models are usually employed. The
approach we are advocating consists in a suitable coupling of the above mentioned models by solving the more expensive models only in the regions of
the domain where it is strictly necessary. For instance, let us consider a river
bifurcation: one can use a 1D model before and after the bifurcation and a
2D one in correspondence of the bifurcation itself. In this talk we present
a strategy to couple the 2D and 1D shallow water models. Starting from a
stability analysis of the two models we derive suitable matching conditions.
Finally some numerical results are provided to assess the effectiveness of the
proposed approach.
Animating Water Waves Using Semi-Lagrangian Techniques
M. El-Amrani (Univ. Rey Juan Carlos), M. Seaid (TU Darmstadt)
Friday, 15:55–16:15, Hall 13
We present a comprehensive methodology for realistically animating water
waves. Our approach is based on the shallow water equations which result
from the depth averaged incompressible Navier-Stokes equations and consequently describe water motion. The method we propose in our talk consists
of an Eulerian-Lagrangian splitting of the equations along the characteristic
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curves. The Lagrangian stage of the splitting is treated by a non-oscillatory
modified method of characteristics, while the Eulerian stage is approximated
by an implicit time integration scheme using finite difference method for
spatial discretization. The combined two stages lead to a semi-Lagrangian
method which is robust, second order accurate, and simple to implement for
problems on complex geometry. In addition, large time steps, shape preserving and mass conservation are properties that characterize our algorithm.
Computational results are shown for several test problems on animating water
flow in bounded pools with and without obstacles. The method is also used to
simulate objects drifting with the water. For instance, to visualize the results
we use massless-particles tracing.
Eigenvalue Problems in Periodic Surface Acoustic Wave Filter
Simulations
S. Zaglmayr (Institute of Computational Mathematics, Johannes Kepler
University Linz)
Surface acoustic wave filters are widely used for frequency filtering in
telecommunications. These devices mainly consist of a piezoelectric substrate with periodically arranged electrodes on the surface. The periodic perturbation by the electrodes introduces a splitting of the frequency domain
in stop-bands and pass-bands. This means only piezoelectric waves excited
at frequencies belonging to the pass-band-region can pass the devices undamped.
The goal of the presented work is the numerical calculation of so-called ”dispersion diagrams”, the relation between excitation frequency and a complex
propagation parameter, where the latter describes damping factor and phase
shift per electrode.
The mathematical model is governed by two main points, the underlying periodic structure and the indefinite coupled field problem due to piezoelectric
material equations. Applying Floquet-Bloch theory for infinite periodic geometries yields a unit-cell problem with quasi-periodic boundary conditions
including the unknown propagation parameter. We present two ways of extracting a frequency-dependent eigenvalue problem describing the dispersion
relation.
Reducing the unit-cell problem only on unknowns on the periodic boundary implies a small-sized quadratic eigenvalue problem which is solved by
QZ-methods. The second method leads to a large-scaled generalized nonhermitian eigenvalue problem which is solved by Arnoldi methods.
The effect of periodic perturbations in computation geometries is confirmed
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249
by numerical experiments. Moreover, we present simulations of high frequency SAW-filter structures which as used in TV-sets and mobile phones.
250
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Posters
Modelling and simulation of the biosensor response under different conditions of solution stirring (R. Baronas) . . . . . . . . . . . . . . . . . . . .
A Three-Phase Model for Wet Pressing of Paper (D. Bezanovic) . . . . . . .
The structure modeling of material composed of the orthortropic crystals (F.
Ivanauskas) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Homogenization Techniques for catalysis in industrial reactor. (S. Lacharme)
A filtered renewal process as a model for a river flow (M. Lefebvre) . . . . .
Deformable Porous Media (K. Malakpoor) . . . . . . . . . . . . . . . . . .
Nonlinear stochastic dynamics by path integration (E Mo) . . . . . . . . . .
Stability and Evolution of Gravity-Driven Porous Media Flows (Applied to
Ecological and Hydrological Problems) (G.J.M. Pieters) . . . . . . . . . .
Evaluation of hygienic environmental indexes in village schools of Mazandaran state (B. Shabankhani) . . . . . . . . . . . . . . . . . . . . . . . .
Solving Flow of ODE with Discrete Velocity Field (B. Tasic) . . . . . . . .
Robust calibration of an electronic nose to assess quality defects of olive oils
(M. Zarzo) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Identification of shifts in a wastewater treatment process with block-wise
PCA and CUSUM charts (M. Zarzo) . . . . . . . . . . . . . . . . . . . .
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Modelling and simulation of the biosensor response under different conditions of solution stirring
R. Baronas (Vilnius University), F. Ivanauskas (Vilnius University), J.
Kulys (Gediminas Technical University)
Biosensors are devices that are based on a biological entity that recognises
an analyte and the transducer that translates the biorecognition event into an
electrical signal. The amperometric biosensors measure the current on an indicator electrode due to direct oxidation of the products of the biochemical reaction. The amperometric biosensors are reliable, relatively cheap and highly
acceptable for environment, clinical and industrial purposes. A mathematical
model of amperometric biosensors has been developed to simulate the biosensor response in stirred and non-stirred solutions. The biosensor is considered
as a plain electrode, containing a membrane with immobilised enzyme applied onto the electrode surface. The model is based on reaction-diffusion
equations containing a non-linear term related to Michaelis-Menten kinetic
of the enzymatic reaction. The model involves three regions: the membrane
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251
where enzyme reaction and mass transport by diffusion takes place, a diffusion limiting region (the Nernst diffusion layer) where only a mass transport
by diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using digital simulation the influence of the
thickness of the enzyme membrane and the diffusion layer on the biosensor response was investigated. The effect of the thickness of the diffusion
layer on the steady-state current considerably depends on that either the enzyme kinetics or the diffusion controls the response. The intensity of stirring
changes the maximal current up to several times. This paper also investigates
the conditions when the mass transport outside the enzyme membrane may
be neglected to simulate the biosensor response in well-stirred solution. The
effect of the Nernst diffusion layer on the biosensor response was evaluated
for different conditions of the enzymatic reaction and types of mixers. The
digital simulation was carried out using the finite difference technique.
A Three-Phase Model for Wet Pressing of Paper
D. Bezanovic (Technische Universiteit Eindhoven), C.J. van Duijn (Technische Universiteit Eindhoven), E.F. Kaasschieter (Technische Universiteit Eindhoven)
As paper passes through the press nip of a paper machine, a pressure pulse is
applied to squeeze water out of the paper web into the felt. This process influences significantly the total drying time, so even small improvements in its
efficiency are highly important. Since experimental approaches are very limited, mathematical modeling and simulation can be of great use. We consider
both the paper web and the felt as two deformable, perfectly elastic porous
media. Motivated by scaling arguments, only transversal flow is considered.
The water and solid phase is assumed incompressible while air is assumed
to be an ideal gas. Material co-ordinates are used to fix the computational
domain. The resulting mathematical model is a parabolic-hyperbolic system
of two non-linear partial differential equations with saturation and void ratio
as primary unknowns. The particularity of the model are jump conditions at
the interface between paper and felt. Computational results are obtained by
combining finite volumes and the explicit Euler method. In the special cases,
when the layers are completely filled with either incompressible fluid (water) or compressible fluid (air), existence and the uniqueness as well as some
qualitative properties of the solution are proven. The future work will be concentrated on the mathematical analysis of the general (three phase) model.
252
Posters
The structure modeling of material composed of the orthortropic crystals
F. Ivanauskas (Vilnius University), F. Ivanauskas (Vilnius University), V.
Skakauskas (Vilnius University), J. Dabulyte (Vilnius University)
Modeling of short wave propagation process is of key importance for solution of very different problems. The measurement methods based on wave
phenomena present an important and challenging field of wave modeling applications. Identification and recognition of defects in continuous structures,
detection of impurity particles or coagulation centers in liquids, recognition
of geometric shapes of objects by measuring reflections of waves, etc., can
be mentioned as examples. The term ’short wave’ is actually the matter of
a scale, however, it is usually understood that the length of the short wave
is hundreds or thousands times less than the dimensions of the structure in
which the propagation of the wave is analyzed. The inherent distortions of
propagating short wave in discrete meshes usually are avoided by using very
dense meshes that requires huge computational resources. The main difficulties arising in ultrasonic measurement process simulation are caused by:
(a) computational models of very large dimensionality, (b) very large number
of time integration steps, (c) adequacy of continua-based models to reality.
We consider the ultrasonic wave propagation problem taking into account
the structure of composites. More precisely, we examine a linearly elastic
composite medium which consists of a matrix containing a set of orthotropic
crystals with the random orientation of the anisotropy axes. By determining
the effective elastic moduli we replace the composite medium by the homogeneous elastic structure. Results of the numerical investigation of the ultrasonic waves propagation and their interaction with a free boundary in 2-D
case will be discussed. References 1. S.H.Ju, Y.M.Wang, Time-dependent
absorbing boundary conditions for elastic wave propagation, Int. J.Meth.
Eng., 50, 2159-2174 (2001). 2.V.A.Buryachenko, N.J. Pagano, R.I. Kim,
J.E. Spowart, Quantitative description and numerical simulation of random
microstructure of composites and their effective elastic moduli, Int. J. Solids
and Structures 40,47-72 (2003).
Homogenization Techniques for catalysis in industrial reactor.
S. Lacharme (Institut for Applied Mathematics, Heidelberg)
Homogenization of partial differential operators is a branch of the theory of
differential equations and mathematical physics which appeared about three
decades ago. Its development was greatly stimulated by various problems
arising in mechanics, physics, and modern technology such that chemical
engineering. Here, I describe the model of an adiabatic packed bed reactor,
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whether it possesses porous or non porous pellets, using homogenization in
the derivation of the equations which describe the cell problem.
Case with non porous pellets: Though, the whole medium (the reactor) can
be consider as porous.The first model that I give is derived from the classical
homogenization for a reactive flow in porous medium. It has been studied in
[1]. Thanks to the proof of convergence, we can conclude that both models
(micro- and macro-) defined in [1] can be applied to our situation and describe
in a very global way our reactor. Still in this case, some phenomenon of nonlinear adsorption are left to study.
Case with porous pellets: Here, we get a phenomenon of multiple scales
that I translate by a model using coupled systems. I consider first an already
derived Darcy system inside of the pellets and a Stokes system concerning
the bed of pellets. This concerns of course the fluid part. Dealing with the
chemical part, I use the same derivation made in [1] but paying a very high
attention to the interface conditions between the two systems, to conserve
the ’power’ of adsorption at the surface part though our pellets are already
’homogenized’.
[1] Hornung U., Jaeger W., Diffusion, Convection, Adsorption and Reaction of
Chemicals in Porous Media, Journal of Differential Equations, Heidelberg, 1992.
[2] Wijngaarden R., Kronberg A., Westerterp K., Industrial catalysis, WILEY-VCH,
Weinheim 1998.
A filtered renewal process as a model for a river flow
M. Lefebvre (Ecole Polytechnique de Montreal)
Models based on a filtered Poisson process are used for the flow of a river.
The aim is to forecast the next peak value of the flow, given that another peak
was observed not too long ago. The most realistic model is the one when the
time between the successive peaks does not have an exponential distribution,
as it is often assumed. An application to the Delaware River in the United
States is presented.
Deformable Porous Media
K. Malakpoor (Technische Universiteit Eindhoven), E.F. Kaasschieter
(Technische Universiteit Eindhoven), C.J. van Duijn (Technische Universiteit Eindhoven)
The swelling and shrinking behavior of cartilaginous tissues (like intervertebral disk) can be modelled by a four component mixture theory in which
a deformable and charged porous medium is saturated with a fluid with dissolved ions. This theory results in a coupled system of non-linear parabolic
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Posters
differential equations together with an algebraic constraint for electroneutrality. There are two major phases of cartilage tissue. A fluid phase containing
liquid and electrolytes (cations and anions) and a solid phase containing collagen fibers and protoeglycans. The solid can shrink only by expelling the
water and can swell only by attracting the water. The mixture theory can be
used for modelling of this phenomena in the frame work of thermodynamics. Finite element has been implemented for the stress relaxation and free
swelling experiments.
Nonlinear stochastic dynamics by path integration
E Mo (Norwegian University of Science and Technology), A. Naess (Norwegian University of Science and Technology), H.C. Karlsen (Norwegian University of Science and Technology)
Stochastic differential equations are used in a variety of different fields, including financial mathematics, turbulence, dynamical systems, and population studies in biology. Solving these systems is often cumbersome and time
consuming, even numerically. The deterministic part of the differential equation could be highly nonlinear, and result in chaotic behaviour. Introducing
white or filtered noise gives a much more realistic model for applications. In
some cases this will also change the behaviour of the system radically.
Many different methods have been proposed to solve or study stochastic
systems. Here, a path integration method is presented together with various
results. The method have shown good estimation also of the tails of the distribution in just a few iterations, and it works well for time dependent systems.
With efficient programming of time steps and interpolation, it is now possible
to solve systems with up to six dimensions with acceptable accuracy.
The poster presentation contains many images comparing deterministic and
stochastic systems, illustrating both stationary and periodic behaviour. Some
applications are also presented, from parameter estimation in stock markets
to ocean wave dynamics.
Stability and Evolution of Gravity-Driven Porous Media Flows (Applied
to Ecological and Hydrological Problems)
G.J.M. Pieters (Technische Universiteit Eindhoven), C.J. van Duijn (Technische Universiteit Eindhoven), P.A.C. Raats (Technische Universiteit
Eindhoven), R.A. Wooding (CSIRO)
A. Fully saturated porous media
Upflowing salty groundwater, evaporating completely at the ground surface, leads to the buildup of a saline boundary layer below the surface. This
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255
boundary layer, if stable, may grow to finite thickness at equilibrium. A similar situation occurs in a periodically heated/cooled peat moss layer, where
a thermal boundary layer is formed due to the temperature cycles. In each
of these cases we have a fluid layer that differs in density from the fluid below, and the question of gravitational stability of this boundary layer arises.
From numerical and Hele-Shaw cell experiments, it appears that the saline
boundary layer may be unstable to perturbations, resulting in so called ”saltfingers”. Similarly, the temperature cycles in a peat moss layer give rise to
convective low and transport. This is also supported by experimental observations. Two paths are followed to analyse stability: the variational energy
method and the method of linearised stability. Both methods give (different)
stability bounds in terms of the system parameters.
B. Unsaturated porous media
Fingering is one form of preferential flow resulting from instability of infiltration through the unsaturated zone. However, we show for two particular
soil classes that these preferential flow paths cannot originate from instabilities of steady, vertical upward or downward flows in homogeneous, unsaturated porous media.
Evaluation of hygienic environmental indexes in village schools of Mazandaran state
B. Shabankhani (Mazandaran University of medical science)
The effect of schools on education and development of humans is very important and schools are the center of concern in many societies. In this descriptive
study, 102 village schools of Mazandaran state were sampled by environmental hygienic during 2 months. Data collection was done questionnaire, measurement and observation of determinations. 62.7% of schools were primary,
36.3% were intermediate and 6.9% were high schools. 33.3% girl schools,
30.4% boy school and 36.3 were mix split shifts for boys and girls. Average
area of each village schools was 3650m 2 . 17.6%of each school was below
standard area level for student. In 14.7% of schools drinking cup and WC
were separate. In 42% of classes light radiation angle was correct. Average
number of classes in each school was 6 with the average 27.8m 2 and 18 students in each class that results 1.54m 2 for each student. Variances were very
big and there are not any programs in my country. Average distance between
schools and road is 3265m but 48% of these schools were below standard
distance.
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Solving Flow of ODE with Discrete Velocity Field
B. Tasic (Technische Universiteit Eindhoven), R.M.M. Mattheij (Technische Universiteit Eindhoven)
For an autonomous problem
dx
= v(x),
dt
where x(0) is any point of a set I(0) say, the solution x is called a flow. If the
velocity field is not given explicitly, i.e. it is known at some points only, the
problem is an ODE with the discrete velocity field. Sources of such fields:
• Experimentally obtained data,
• Numerical solution coming from PDE or another ODE
For stiff problems one needs implicit method to find the solution without
stability constraints. In this project we exploit the autonomous character of
the ODE and derive explicit methods having the same favourable stability
properties.
The example which illustrates the so-called flow method concerns a DC
motor electrical circuit with a nonlinear resistor as a current-protection element.
Robust calibration of an electronic nose to assess quality defects of olive
oils
M. Zarzo (Polytechnic University of Valencia), A. Gutiérrez (Inst. Valenc.
Invest. Agrarias), E. Moltó (Inst. Valenc. Invest. Agrarias)
The quality of many products is related with their olfactive perception and can
be assessed by a sensory panel, but this procedure is slow and expensive. An
attempt to overcome these drawbacks is to use electronic devices that generate
signals related with the chemical composition of the volatiles. These systems,
properly calibrated with statistical methods, are able to assess the aroma of
different products, and for this reason they are called electronic noses.
Olive oils are classified according to the aroma. Two important defects to
be assessed are the rancid and winey attributes. A set of 26 samples has been
prepared with increasing intensities of both defects. These samples have been
assessed by a panel of trained tasters, and afterwards by an aroma sensor.
From every sample, the system records for 8 minutes the evolution of an
electric signal from 8 metal oxide semiconductor gas sensors, with a sampling
rate of 1 Hz. Hence, the data matrix to analyse contains 26 samples and 3840
variables.
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257
To predict the intensity of the defects from the signals acquired with the
sensors, different multivariate calibration methods can be used. But these
signals suffer drifts from sample to sample, what reduces the predictive ability of the models. A calibration method, robust against drift, is proposed. It
involves the parameterisation of signals from gas sensors with different nonlinear equations and 39 parameters are obtained from every sample. With
these parameters a PLS regression has been conducted, that classifies properly the samples according to the type of the defect, except for low intensities.
Although sensory panels will always be necessary, electronic noses properly
calibrated will be a complementary tool in the quality control of many products in the future.
Identification of shifts in a wastewater treatment process with block-wise
PCA and CUSUM charts
M. Zarzo (Polytechnic University of Valencia), R. Barat (Polytechnic University of Valencia), L. Borras (Polytechnic University of Valencia), J.
Ferrer (Polytechnic University of Valencia)
Historical data from a Sequencing Batch Reactor (SBR) operated for biological phosphorus removal in waste waters have been analysed. It is a batch process in three stages per cycle that take place in the same reactor. During stage
1, that lasts 1.5 hours, phosphorus is released by polyphosphate accumulating
organisms (PAOs) in anaerobic conditions. Afterwards PAOs carry out phosphorus uptake in a second stage for 3 hours in aerobic conditions. Finally, the
activated sludge is settled for 1.5 hours. During the process five parameters
are registered on line by means of electronic sensors: electric conductivity,
redox potential, dissolved oxygen concentration, pH and temperature.
A historical data set of 70 cycles has been analysed, corresponding to a
period of 3 months. As the duration of all cycles is the same, data from every
sensor are structured in a matrix of 70 cycles by 356 instants of time. This
data set has been analysed with block-wise PCA, conducting a PCA with every block of variables formed by the trajectory of one sensor in one stage.
For the 15 PCA models carried out, the statistically significant components
have been obtained by crossvalidation, and the associated latent variables.
These new variables summarise the information of the sensor along the stage.
Afterwards, a CUSUM chart has been conducted with every latent variable,
accumulating the values according to the order of the cycles. Overlapping all
CUSUM charts in a same figure, several shifts in the process are clearly identified, and also the relationships among the signals from the sensors. In order
to identify the causes that originate those shifts it is very useful to compare
the weights and the trajectories of the variables in the different models, and to
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check these results with the technical information available from the process.
Index
259
Index
Upright numbers refer to presentations and posters, italics to co-authorships;
bold numbers are minisymposium organizers.
A
Aa, N.P. van der . . 133
Aarnes, J E . . . . . . 23
Abrukov, V. . . . . . . 84
Agterof, W.G.M. . . 120
Aissani, A. . . . . . . 238
Akker, H. van den . 121
Allaart-Bruin, S.M.A. 97
Allgöwer, F. . . . . . . 43
Almendral Vazquez,
A. . . . . . . . . . 189
Alshin, A.B. . . . . . 110
Alshina, E. . . . . . . 109
Andonowati, A. . . 219
Anile, A.M. . . . . . 231
Anthonissen, M.J.H. 74,
75
Araújo, A. . . . . . . 111
Arens, K. . . . . . . . . 61
Argentini, G. . . . . 235
Arickx, F. . . . . . 20, 23
Aslanyan, A.G. . . . 134
Atzema, E.H. . . . . . 56
B
Bagchi, A. . . .
Bailly, C. . . . .
Barat, R. . . . .
Baronas, R. . .
Barsky, E. . . .
Bartel, A. . . . .
Basermann, A.
Bastian, P. . . .
Beck, S.B.M. .
Bermúdez, A. .
Bernal, F. . . . .
Bernardo, M. di
Berridge, S.J. .
Bezanovic, D. .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. 147
. . 48
. 257
. 250
. 178
40, 116
. . . 92
. . . 54
. . 226
. . 185
. . 111
. . . 32
. . . 128
. . . 251
Bezdek, M. . . . . . 199
Bielinski, A. . . . . . . 53
Bijl, H. . . . . . . . . 149
Birnir, B. . . . . . . . 169
Bisgaard, S. . . . . . . 89
Blackmore, D. 239, 240
Blom, C.P.A. . . . . 154
Blom, J.G. . . . . . . 128
Boelens, O.J. . . . . 152
Bondar, M.L. . 133, 133
Bongers, H. . . . . . 174
Bonilla, L.L. . 166, 167,
168
Borras, L. . . . . . . 257
Boudovis, A.G. . . . 119
Bratov, V. . . . . . . 187
Brennan, C. . . . . . . 21
Breun, S. . . . . . . . 176
Briels, W.J. . . . . 46, 47
Brown, A. . . . . . . 106
Bruin, I.C.C. de 194, 194
Bruining, J. . 49, 51, 51
Brunet, G. . . . . . . . 36
Brunone, B. . . . . . 225
Buikis, A. . . . . . . 245
Büskens, C. . . . . . . 59
C
Callies, R. 176, 176, 243
Camp, O.M.G.C. op
den . . . . . . . . . 184
Cant, R.S. . . . . . . 233
Carrillo, J.A. . . . . . 39
Cepitis, J. . . . . . . 210
Chapman, S.J. . . . 245
Charlier, E. . . . . . 148
Charpin, J.P.F. . . . 245
Chiang, H. . . . . . . 182
Chou, R. . . . . . . . . 92
Christiansen, P.L. . 198
Chudej, K. 143, 145, 146
Clason, C. . . . . . . 198
Class, H. . . . . . 53, 139
Clopeau, T. C. . . . 214
Condon, M. . . . . . . 21
Coutelieris, F.A. . . 118,
120, 179
Covas, D. . . . . . . . 226
Creemers, T. . . . . . 108
Cromme, J. . . . . . 241
Cuesta, C.M. . . . . . 27
Cumberbatch, E. . . 132
D
Dabulyte, J. . . . . . 251
Dahoe, A.E. . . . . . 233
Damme, R.M.J. van 153
Danilov, D.L. . 101, 102
Das, K. . . . . . . . . . 63
Dauwe, R.M. . . . . . 30
De Pierro, A.R. . . . 243
Deconinck, J. . . . . . 95
Dell’Acqua, G. . . . 167
Deschrijver, D. . . . . 20
Deuschle, T.D. . . . 204
Dhaene, T. . . . . . 20, 23
Diehl, M. . . . . . . 34, 42
Dimier, A. . . . . . . 106
Doelder, C.F.J. den 186
Dolezel, V. . . . . . . 216
Dorn, O. . . . . . . . . 79
Driessen, J.N. . . . . . 82
Driessen, L.T. . . . . . 55
Duffy, B.R. . . . 85, 109
Duijn, C.J. van . 28, 49,
50, 51, 251, 253, 254
Duivesteijn, G.F. . . 149
Dumbrajs, O. . . . . 210
260
Index
E
Edwards, C. M. . . . 132
Eijndhoven, S.J.L.
van . . . . . . . . . 100
El Guennouni, A. . 129
El-Amrani, M. . . . 247
Ellsasser, C. . . . . . 178
Engell, S. . . . . . . . . 34
Eppler, E.K. . . . . . 200
Ertler, C. . . . . . . . 167
Escobedo, R. . 111, 167,
168
Eyres, R.D. . . . . . . 32
F
Faraco, G. . . . . . . 231
Fasano, A. . 71, 72, 242
Ferket, P.J.J. . . . . . 125
Ferrante, M. . . . . . 225
Ferreira, J.A. . . . . 111
Ferrer, A. . . . . . . . 181
Ferrer, J. . . . . . . . 257
Figarella, T. . . 101, 101
Findeisen, R. . . . . . 43
Fitt, A.D. . . . . . . . 107
Fledderus, E.R. 194, 195
Foucault, G. . . . . . 157
Francois Corrihons,
F.C. . . . . . . . . 106
Franke, R. . . . . . . . 45
Fuhrmann, J. . . . . . 94
Fujino, S. . . . . . . . 209
Fusek, P. . . . . 121, 123
Fusi, L. . . . . . . . . . 72
G
Gaertner, K. . . .
Gaeta, G.A. . . .
Gawin, D. . . . .
Gelder, D. . . . .
Gerstmayr, J. . .
Geurts, B.J. . . .
Gheorghiu, I. . .
Giniatoulline, A.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. 94
230
. 19
123
206
175
. 61
215
Gjonaj, E. . . . . . . 141
Gnnther, M. . . . . . 146
Goetz, T.G. . . . 32, 212
Goey, L.P.H. de 174, 233
Gol’dshtein, V. . . . 180
Goldfarb, I. . . . . . 180
Gómez, D. . . . . . . 185
González, P. . . . . . . 78
Gonzalez Padilla, F.J. 97,
187
Gonzalez, M. . . . . 216
Goossens, J.G.C.M. 108
Graf, H. . . . . . . . . 156
Grasso, G. . . . . . . 231
Graziadei, M. . . . . 174
Griebsch, S. . . . . . 147
Groenen, P.J.F. . . . 188
Grubisic, I . . . . . . 106
Günther, M. . . . 71, 143
Gutiérrez, A. . . . . 256
H
Haagh, G.A.A.V . . 120,
184
Haase, G. . . . . . . . . 62
Hagmeijer, R. . . . . 154
Hall Taylor, N. . . . 107
Halse, C.K. . . . . . . 32
Harbrecht, H. . . . . 200
Hassanizadeh, S. M. 28
Hazra, S.B. . . . . 53, 55
Hegen, D. . . . . . . 184
Heidebrecht, P. . . . 144
Heijden, J.W.J.M. van
der . . . . . . . . . . 58
Heiliö, M. . . . 229, 232
Heinsbroek, A. . . . 108
Helmig, R. . . . . . . 139
Hemker, P.W. . . . . 151
Hendrickx, W. . . 20, 23
Heres, P.J. . . . . . 20, 22
Hermann, M. . . . . 218
Hilbers, P.A.J. . . . . 130
Hinch, J. . . . . . . . . 39
Hjorth, P.G. . . . . . 131
Hoemberg, D. . . . . . 74
Holden, H. . . . . . . . 82
Hömberg, D. . . . . . 75
Honkala, M. . . . . . . 69
Hooda, D.S. . . . . . 104
Horváth, R. . . . . . 143
Houben, S.H.M.J. 91, 92
Houweling, P. . . . . 126
Huerta Cerezuela, A. 182
Hulsen, M.A. . . . . . 49
Hulshoff, S.J. . . . . 155
Hulsken, G. . . . . . 101
Hunt, J. . . . . . . . . 166
Hwang, W.R. . . . . . 49
I
Iliev, O. . . 202, 227, 227
Iori, G. . . . . . . . . 187
Iovane, G. . . . . . . 230
Iske, A. . . . . . . . . . 24
Ivanauskas, F. . 250, 251,
251
Ivanov, R. . . . . . . . 21
J
Jaekel, U. . . . . . . . 92
Jaffré, J. . . . . . . . . 54
Jakobs, H. . . . . . . 139
Jamshidian, F. . . . . 147
Janoske, U. . . . . . 204
Jansen, M.H. . . . . 201
Janssen, J. . . . . . . 118
Janssen, J.H.J. . . . . 58
Janssen, M.J.J. . . . 127
Jenny, P. . . . . . . . . 25
Jordaan, E.M. 29, 82, 182
Juanes, R. . . . . . . . 26
Junk, M. . . . . . . . 209
Jussilainen Costa, L.R.
de . . . . . . . . . . 116
K
Kaasschieter, E.F. . 251,
253
Index
Kadam, J. V. . . . . . . 44
Kagan, P. . . . . . . 96, 98
Kalis, H. . . . . 210, 245
Kalitkin, N.N. . . . . 109
Kaltenbacher, B.K. 183,
196
Kanavouras, A.K. . 179,
179
Kar, R.C. . . . . . . . 136
Karanko, V. . . . . . . 69
Karkhin, V. . . . . . . 59
Karlsen, H.C. . . . . 254
Käser, Martin . . . . . 24
Katz, D. . . . . . . . 180
Kenett, R.S. . . . . . . 30
Kerimbekov, M. . . 236
Keunings, R. . . . 46, 48
Kharytonov, A.A. . 160
Kheireldin, A.M. . . 240
Kim, W.-J. . . . . . . 211
Kindelan, M.K. . . 77, 78
Kippe, V. . . . . . . . . 24
Klar, A. . . . . . . . . 159
Knorr, S. . . . . . . . 118
Koenders, C. . 202, 227
Koenders, M.A. . . 204
Kordon, A.K. . . . . 182
Koren, B. . . . . 149, 170
Koryagina, A.B. . . 109
Kowar, R. . . . 196, 197
Kozyreff, G.P. . . . . 123
Kraaij, M.G.M.M.
van . . . . . . . . . 135
Kroll, N. . . . . . . . 222
Kroot, J.M.B. . 141, 142
Krüger, K. . . . . . . . 45
Kruse, L. . . . . . . . . 92
Kühn, C. . . . . . . . 147
Kulys, J. . . . . . . . 250
Kuz’min, A.G. . . . 234
Kværnø, A . . . . . . 116
L
Lacharme, S. . . . . 252
261
Ladoucette, S.A. . . 103,
103
Lambert, M.F. . . . 224
Laptev, V. . . . . . . 227
Latz, A. . . . . . 202, 227
Latz, A.L. . . . . . . 203
Lee, M.E.M. . . 107, 109,
135
Lee, S. . . . . . . . . 211
Leemput, P. van . . 129
Leentvaar, C.C.W. . 189
Leese, R.A. . . . . . . 83
Lefebvre, M. . . . . 253
Leineweber, D.B. . . 34
Leon, J.C. . . . . . . 157
Leygue, A. . . . . . . . 48
Li, L. . . . . . . . . . 223
Lie, K.-A. . . . . . 23, 24
Lindner, E.H. . . . . . 62
Lionheart, W.R.B. . 208
Litjens, R. . . . 194, 196
Loch, H. . . . . . . . 122
Lord, R. . . . . 125, 127
Luppes, R. . . . . . . 171
M
Maamoun, A. . . . .
Mackey, D. . . . . .
Madalina Rusu, MR
Majka, A. . . . . . .
Majorana, A. . . . .
Maksimov, P.V. . . .
Malakpoor, K. . . .
Malinin, G.I. . . . .
Mancini, A. . . . . .
Mangold, M. . . . .
Manson, N.W. . . .
Mansutti, D. . . . . .
Mantel, O. . . . . . .
Marchesin, D.M. . .
Marheineke, N. . . .
Marin, P. . . . . . . .
Markvoort, A.J. . .
Marquardt, W. . . .
240
. 86
242
. 35
. 39
158
253
. 84
242
145
. 85
161
195
. 50
185
157
130
. 44
Maten, E.J.W. ter 68, 90,
91
Matic, D. . . . . . . . 195
Mattheij, R.M.M. 75, 98,
255
Maubach, J.M.L. . . 149,
169, 169
Meijer, H.E.H. . . . . 49
Meniconi, S. . . . . . 225
Miglio, E.M. . 246, 247
Mikelic, A.M. . 213, 214
Mincheva, I. . . . . . 244
Mishra, R. . . . . . . 136
Mo, E . . . . . . . . . 254
Mockus, J. . . . . . . 232
Mohammay, A.R. . . 84
Mohdeb, Z. . . . . . . 35
Mohr, M. . . . . . . . 237
Moiseenko, D.D. . . 158
Mokkadem, A. . . . . 35
Molenaar, J. . . . . 46, 47
Moltó, E. . . . . . . . 256
Montes, C. . . . . . . . 77
Mooiweer, G.D. . . . 30
Morozov, E.V. . . . 213
Morsche, H.G. ter . 200,
200, 224
Moscoso, M. . . . . . 79
Movchan, A.B. 134, 179
Movchan, N.V. . . . 179
Muscato, M. . . . . . 168
Muscato, O. . . . . . 167
Muzzioli, S. . . . . . 104
Myers, T.G. . . . . . 245
N
Naess, A. . . . .
Nagy, K. . . . .
Nassehi, V. . . .
Nedea, S.V. . .
Nekka, F. . . . .
Neunzert, H. . .
Nordhausen, M.
.
.
.
.
. . 254
. . . 43
. . 228
. . 130
223, 223
. . 32, 83
. . . 92
262
Index
Notten, P.H.L. . . 93, 94,
102
O
O’Dwyer, A. . .
Ochs, S.O. . . . .
Ockendon, H. .
131, 132, 135
Oliveira, P. de . .
Olshanskii, M.A.
Oosterlee, C.W.
Oriols, X. . . . .
Ovenden, N.C. .
Overweg, J.A. . .
Ózdemir, H. . . .
. . . 85
. . . 53
82, 131,
.
.
.
.
.
.
.
.
.
.
.
.
.
.
111
172
189
. 41
132
142
154
P
Pajovic, P. . . . . . . 195
Panda, L. . . . . . . . 136
Pantano, P. . . . . . . 231
Papageorgiou, L.G. 105
Park, S. . . . . . . . . 211
Parrott, K. . . . . . . 189
Pavlov, R.I. . . . . . . 84
Perez Foguet, A. . . 182
Perner, P. . . . . . . . . 31
Perotto, S.P. . . 246, 247
Pesavento, F. . . . . . 19
Pesch, H.J. . . . . 59, 145
Petzet, V. . . . . . . . . 59
Piesche, M.P. . . . . 204
Pieters, G.J.M. . . . 254
Pietersz, R. . . 106, 188
Please, C.P. . . . . . 107
Pohjolainen, S.A. . 229
Polyakov, M.V. . . . 217
Pop, I.S. . . . . . 27, 244
Pop, S.R. . . . . . . . 211
Potapov, V.D. . . . . 235
Pothof, I. . . . . . . . 108
Pousin, J. . . . . 213, 214
Prada, C. de . . . . . . 46
Prek, V. . . . . . . . . 201
Prikhodovsky, A. . . . 59
Primicerio, M. . . . 242
Procházka, P. . 216, 233
Prodan, A. . . . . . . 242
Prykarpatska, N.K. 239
Prykarpatsky, K. 239, 240
Prykarpatsky, Y.A. . 240
Pulch, R. . 70, 116, 118
Pyle . . . . . . . . . . 107
Q
Quak, E.G. . . . . . . 155
R
Raalte, M.H. van . . 151
Raats, P.A.C. . . . . 254
Raffo, R. . . . . . . . 161
Ramon, H. . . . . . . 204
Ramos, H. . . . . . . 226
Rasmussen, A.R. . . 198
Rathberger, Ch. . . . . 62
Remus Campean, RC 242
Rentrop, P. . . . . . . . 61
Reynaerts, H. . . . . 104
Rieder, A. . . . . . . 199
Rietman, R. . . . . . 195
Rinaudo, S. . . . . . . 40
Roberts, J.E. . . . . . . 54
Rogers, L.C.G. . . . 115
Romano, V.R. . . . . 209
Romero, O. . . . . . 169
Rommes, J. . . . . . . 91
Roos, J. . . . . . . . . . 69
Roose, D. . . . . . . 129
Rossen, W.R. . . . 50, 50
Rossow, C. . . . . . . 222
Rottschäfer, V. 131, 132
Rout, S. . . . . . . . . 189
Roy, D. . . . . . . . . . 33
Ruggeri, F. . . . . . . . 90
Ruziwa, W.R. . . . . 228
S
Sacco, S.R. . . . . . 117
Saleri, F.S. . . . 246, 247
Salerno, S.A. . . . . 230
Salgado Rodriguez,
P. . . . . . . . . . . 185
Samaey, G. . . . . . 129
Santi, R. . . . . . . . 161
Sarabia, D. . . . . . . . 46
Sargolzaei, P. . . . . . 84
Sarkis, M. . . . . . . . 50
Schaerer, C.E.S. . . . 50
Schanzer, G. . . . . . 243
Schilders, W.H.A. 20, 41
Schloeder, J.P. . . . . 34
Schrefler, B. . . . . . . 19
Schuhmann, R. . . . 141
Schulz, V. . . . . . 53, 55
Schumacher, J.M. . 125,
128
Schürrer, F. . . . . . 167
Schwamborn, D. . . 222
Seaid, M. . 159, 216, 247
Seibold, B. . . . . . . . 32
Sellier, M. . . . . . . 122
Selsil, A. . . . . . . . 179
Selsil, O. . . . . . . . 134
Sevat, M.F. . . . . . . . 91
Seyyed, M. . . . . 34, 63
Shabankhani, B. . . 255
Shaposhnikova, E.V. 60
Sheng, M. . . . . . . 145
Siddiqi, A.H. . 223, 223
Siedow, N. . . . 122, 124
Sieniutycz, S. . . . . 208
Simeon, B. . . . 205, 207
Simonin, O. . . . . . 120
Simpson, A.R. . . . 224
Sizov, M. . . . . . . . 170
Skakauskas, V. . . . 251
Skytt, V. . . . . . . . 157
Smaranda Cristea, SC 46
Smith, P.D. . . . . . 177
Smith, W.R. . . . . . . 75
Soleimani, M. . . . . 208
Soler, J. . . . . . . . . 169
Soliman, A.M. . . . 240
Index
Sourdille, P. . . . . 85, 85
Sørensen, M.P. . 31, 99,
198
Speranza, A. . . . . . . 72
Starke, J. . . . . . . . 178
Staszewski, W.J. . . 226
Steenhoven, A.A.
van . . . . . . . . . 130
Stehouwer, H.P. . 55, 57
Sternberg, K. . . . . 145
Sternberg, N. . . . . 175
Stinstra, E.D. . . . . . 57
Stoll, S.O. . . . . . . . 61
Stranges, F. . . . . . 231
Striebel, M. . . . . . . 90
Struckmeier, J.S. . . 212
Stubos, T. . . . . . . 119
Stumpp, Th. . . . . . 207
Sudirham, J.J. . . . . 153
Sun, K.H. . . . . . . 107
Sundmacher, K. . . 144
Suomela, K . . . . . 229
Surulescu, N. . . . . 188
T
Tasic, B. . . . . . . . 255
Tawfiq, H. . . . . . . 217
Teichelmann, G. . . 206
Terenzi, A. . . . . . . . 73
Teugels, J.L. . . . . . 103
Thije Boonkkamp, J.H.M.
ten 133, 161, 172, 173
263
Tiba, I. . . . . . . . . 159
Tijskens, E. . . . . . 204
Tijsseling, A.S. 224, 224
Timokha, A.N. . . . 218
Tobin, P.C. . . . . . . 106
Toumi, A. . . . . . 34, 44
Troeshestova, D.A. . 84
Trofimov, O.E. . . . . 60
Trowbridge, B. . . . . 67
Turner, M.M. . . . . . 86
Turunen, E. . . . . . 229
V
Vasileva, D. . . . . . 227
Vegt, J.J.W. van der 151,
153
Veldman, A.E.P. . . 171
Veltman, K. . . . . . 148
Ven, H. van der . . . 152
Verbitskiy, E.A. . 93, 94
Verboven, P. . . . . . 204
Verhoeven, A. . . . . . 69
Vermolen, F.J. . . . . 51
Verschuere, M. . . . 101
Verwer, J.G. . . . . . 150
Vinogradov, S.S. . . 177
Vinogradova, E.D. . 177
Vladislavleva, J. . 80, 98
Vorst, H.A. van der 150
W
Wackers, J. . . . . . . 170
Waghode, A.N. . . . 228
Wakeman, R.J. . . . 228
Waterman, M. . . . . 194
Wawrenczuk, A. . . . 96
Wegener, R. . . . . . 124
Weiss, W. . . . . . . . 76
Wessels, J. . . . . . . . 81
Westerlund, K.O.J.
105
Williams, J.F. . . . . 128
Wilson, R.E. . . . . . . 32
Wilson, S.K. 63, 85, 109
Winkler, R. . . . . . 238
Wislicki, W.W . . . . 35
Wolff, S. . . . . . . . . 33
Wooding, R.A. . . . 254
Wynn, H.P. . . . . . . 101
Wystup, U. . . . . . . 147
Y
Yevdokymov, D.V.
Yiotis, A.G. . . . .
Yortsos, Y.C. . . .
Young, A. . . . . .
.
.
.
.
217
119
119
226
Z
Zaglmayr, S. . . . . 248
Zarzo, M. 181, 256, 257
Zeltz, E.Z. . . . . . . 213
Zervos, M. . . . . . . 187
Zhu, H. . . . . . . . . 199
Zobory, I. . . . . . . . 86
Zoller, V. . . . . . . . . 86
264
Maps of the Auditorium
map Auditorium — floor 0
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map Auditorium — floors 1 and 2
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Numerical simulation of the problem arising - ECMI 2004

Transcription

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