Student workshop on scientific computing 2016

Department of Mathematics, FNSPE CTU in Prague
Děčı́n, Czech Republic
Student workshop on scientific computing
2016
June 9 - 12, 2016
Conference Information
The scientific colloquium of CTU organized by the Department of Mathematics, FNSPE CTU in
Prague is devoted to the meeting of students and young applied mathematicians dealing with
numerical solution of partial differential equations, mathematical modelling, numerical simulation
of problems in technology, environment, biology and computer science.
Organizers
J. Kukal, Department of Software Engineering, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague
kukal (at) dc.fjfi.cvut.cz
J. Mikyška, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague
jiri.mikyska (at) fjfi.cvut.cz
T. Oberhuber, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague
tomas.oberhuber (at) fjfi.cvut.cz
R. Fučı́k, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague
radek.fucik (at) fjfi.cvut.cz
P. Pauš, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague
petr.paus (at) fjfi.cvut.cz
P. Strachota, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague
pavel.strachota (at) fjfi.cvut.cz
M. Kuchařı́k, Department of Physical Electronics, Faculty of Nuclear Sciences and Physical
Engineering, Czech Technical University in Prague
milan.kucharik (at) fjfi.cvut.cz
Conference office
M. Vostřáková, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague
Organizing committee
J. Kukal, J. Mikyška, T. Oberhuber, R. Fučı́k, P. Pauš, P.Strachota, M. Kuchařı́k
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Additional information
URL: http://geraldine.fjfi.cvut.cz/wsc2016
Venue:
Czech Technical University in Prague, Zámecká sýpka (Castle grange), Nárožı́ 6, Děčı́n, Czech
Republic
Acknowledgement
This workshop was supported by the Grant Agency of the Czech Technical University in Prague,
grant No. SVK 37/16/F4.
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List of Participants
The list of all participants in alphabetical order.
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Name
Craig Adams
Petr Bauer
Michal Beneš
David Celný
Martin Dlask
Pavel Eichler
Jan Franců
Radek Fučı́k
Vı́t Hanousek
Milan Holec
Alison Kathol
Mark Keck
Viera Kleinová
Jakub Klinkovský
Miroslav Kolář
Milan Kuchařı́k
Jaromı́r Kukal
Zachary Mahon
Jiřı́ Mikyška
Jiřı́ Minarčı́k
Matej Mojzeš
Tomáš Oberhuber
Petr Pauš
Ondřej Polı́vka
Chittaranjan Ray
Tomáš Smejkal
Michal Sněhota
Jakub Solovský
Pavel Strachota
Vojtěch Straka
Robert Straka
Tran Quang Van
Daniel Ševčovič
Róbert Špir
Jan Šácha
Alexandr Žák
University / Institute
University of Nebraska
IT CAS
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague, Institute of Physics, AS CR, v.v.i
University of Nebraska
University of Nebraska
SvF STU, Bratislava
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
University of Nebraska
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
Water for Food Institute University of Nebraska
FNSPE CTU in Prague
FCE CTU in Prague
FNSPE CTU in Prague
FNSPE CTU in Prague
FNSPE, CTU in Prague
AGH Krakow
FNSPE CTU in Prague
Comenius University
SvF STU, Bratislava
FCE CTU in Prague
FNSPE CTU in Prague
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Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Student
Scientific Programme
Thursday 9. 6. 2016
14:00 – 14:05
Opening
Chairman: Pavel Strachota
14:05 – 14:35 Milan Kuchařı́k: Multi-Material Remap for Staggered Arbitrary LagrangianEulerian (ALE) Methods
14:35 – 15:05 Jaromı́r Kukal: Useful Discrete Approximations of Laplacian and Gradient
15:05 – 15:30 Matej Mojzeš: Mean Field Lévy Flight as Integer Optimization Heuristics
15:30 – 16:00
Coffee break
Chairman: Jaromı́r Kukal
16:00 – 16:30 Pavel Strachota: A Hybrid Parallel Numerical Algorithm for Three-Dimensional
Phase Field Modeling of Crystal Growth
16:30 – 17:00 Tomáš Oberhuber: TNL: FDM on GPU in C++
17:00 – 17:30 Petr Pauš: Numerical study of spiral motion and tip meandering
17:30 – 18:00 Tran Quang Van: Two-stage Alpha-Stable Distribution Parameters Estimation
Approach
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Friday 10. 6. 2016
07:30 – 09:00
Breakfast (Hotel Faust)
Chairman: Michal Beneš
09:00 – 09:20 Jiřı́ Minarčı́k: Applications of planar and space curve evolution
09:20 – 09:40 Vojtěch Straka: A posteriori error estimates for finite element solutions of Poisson equation
09:40 – 10:10 Robert Straka: Lattice Boltzmann Method and Natural Convection
10:10 – 10:30 Pavel Eichler: Numerical analysis of the Lattice-Boltzmann method in 2D
10:30 – 11:00
Coffee break
Chairman: Jiřı́ Mikyška
11:00 – 11:30 Michal Sněhota: Quantification of trapped gas in dual-porosity media with
continuous and discontinuous domains
11:30 – 11:55 Jan Šácha: Quantitative evaluation of water distribution from two and threedimensional neutron images the during ponded infiltration
11:55 – 12:15 Jakub Klinkovský: A massively parallel implementation of two-phase immiscible
flow in porous media using the mixed-hybrid finite element method
12:15 – 12:35 Jakub Solovský: Mathematical modeling of contaminant transport in porous
media
12:35 – 14:00 Lunch break
Chairman: Petr Pauš
14:00 – 14:30 Radek Fučı́k: Multidimensional exact solution for two-phase flow in porous
media
14:30 – 14:55 Ondřej Polı́vka: Numerical Computation of Two-Phase Compositional Flow in
Porous Media
14:55 – 15:40 Chittaranjan Ray: Managing water for global food security
15:40 – 16:10 Alexandr Žák: Modeling of Water-Ice Interface within Freezing Soil at MicroScale
16:10 – 16:40 Coffee break
Chairman: Robert Straka
16:40 – 17:05 Martin Dlask: On the correlation dimension estimation using rotational spectrum
17:05 – 17:35 Michal Beneš: Spatially Isotropic Approximation Scheme for Motion by Mean
Curvature
17:35 – 18:05 Petr Bauer: Ventilation losses of gearboxes
19:15 – 19:30
Group photo
19:30 – 22:30
Conference dinner (hotel Zlatá Koruna)
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Saturday 11. 6. 2016
07:30 – 09:00
Breakfast (Hotel Faust)
Chairman: Ondřej Polı́vka
09:00 – 09:30 Róbert Špir: Efficient point cloud registration using PCL library
09:30 – 10:00 Viera Kleinová: A numerical method for optical flow
10:00 – 10:25 David Celný: Mathematical modeling of phase interfaces of liquid mixtures using
PC-SAFT equation of state.
10:30 – 20:00 Hiking Excursion
Sunday 12. 6. 2016
07:30 – 09:00
Breakfast (Hotel Faust)
Chairman: Alexandr Žák
09:00 – 09:30 Daniel Ševčovič: Construction of upper bounds of the HOMO-LUMO spectral
gaps by semidefinite relaxation techniques
09:30 – 09:55 Milan Holec: Discontinuous Galerkin High-Order Nonlocal Transport and Energy Equations Scheme for Radiation-Hydrodynamics
09:55 – 10:20 Miroslav Kolář: Numerical Solution of Constrained Curvature Driven Flow
10:20 – 10:50
Coffee break
Chairman: Miroslav Kolář
10:50 – 11:10 Jan Franců: Multicomponent transport model based on the Stefan-Maxwell theory and continuum mechanics
11:10 – 11:30 Tomáš Smejkal: Computation of equilibrium states at constant internal energy,
volume and moles
11:30 – 11:55 Vı́t Hanousek: Template Numerical Library on Intel Xeon Phi
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List of Abstracts
The list of abstracts of all talks and posters in alphabetical order.
Spatially Isotropic Approximation Scheme for Motion by Mean Curvature
Michal Beneš, Jaromı́r Kukal
FNSPE CTU in Prague
Friday 10. 6. 2016, 17:05 – 17:35
The contribution summarizes the knowledge on the planar mean-curvature flow approximated
by the Allen-Cahn equation with the gradient forcing term. An overview on several spatial
discretizations is presented including their advantages and drawbacks. Then a new approach
respecting mesh directions but suppressing their influence on spatial isotropy of the solution
is presented. Besides main idea, namely the obtained numerical results are presented and
discussed.
Mathematical modeling of phase interfaces of liquid mixtures using
PC-SAFT equation of state.
David Celný
Saturday 11. 6. 2016, 10:00 – 10:25
FNSPE CTU in Prague, Institute of Thermomechanics, Academy of Sciences of the Czech Republic
Phase interface is common phenomenon that can be found in each glass of mineral water. It
is beneficial to understand its behavior and use it for more pressing matters such as carbon
capture and storage technologies (CCS). Our work deals with gas-liquid phase interfaces of
two component systems. These systems can form two basic types of phase interfaces on which
we focus, namely planar interface (water level) and spherical interface (bubble). Both types of
interface can be described via density function. One of the main tasks is obtaining molar density
function profiles through minimization of grand potential functional. Our approach is based on
theoretical results from Cahn-Hilliard gradient theory from 1957 that enables transformation of
said problem into system of second order differential equation. Due to the performed simplification
this system can be split into nonlinear algebraic system and one differential equation. Simplified
formulation can be solved and provides resulting molar density function illustrating change of
molar density over the change of coordinate (radius from center of bubble). Chosen approach
requires the knowledge of mixture properties (chemical potential and pressure). These properties
are computed with the PC-SAFT equation of state. We are able to compute the binary mixtures
that exhibit polar interaction (i.e. CO2 ). Due to the unavailability of reference experimental data
we investigated the system comprised of CO2 and CH4 .
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On the correlation dimension estimation using rotational spectrum
Martin Dlask
FNSPE CTU in Prague
Friday 10. 6. 2016, 16:40 – 17:05
Fractal sets are theoretical structures that don’t exist in reality, however, many objects, such
as biomedical or economic data have fractal pattern with noninteger dimension. Therefore it
is necessary to develop methods that would provide unbiased estimation of fractal dimension.
Technique of correlation sum belongs to the family of well-known and simple procedures which
can be used for correlation dimension estimation, nevertheless, it was proven that the obtained
dimension is underestimated. The presentation shows new methodology of correlation dimension
estimation from point sets using rotational spectrum. Our novel approach employs the spectrum
of point set which is averaged via rotation of power pattern. It was proven that the slope of
the power spectrum can be stabilized by means of its rotation in a space with high dimension
and the corresponding dimension estimate is unbiased. Precise correlation dimension estimation
could be used later for data classification or prediction making.The efficiency of proposed method
was tested using Monte Carlo simulation on the sets with known dimension.
Numerical analysis of the Lattice-Boltzmann method in 2D
Pavel Eichler
FNSPE CTU in Prague
Friday 10. 6. 2016, 10:10 – 10:30
In this contribution, numerical simulations based on the Lattice-Boltzmann method (LBM) will
be discussed. First, the kinetic theory with the Boltzmann equation (BE) and some aspects of
the derivation of the LBM from the BE with the BGK approximation of the collision operator will
be introduced. In the last part, the application of LBM to the Hagen-Poiseuille flow between
two infinite parallel plates will be discussed and the numerical results will be compared to the
analytical solution in order to determine the experimental order of convergence.
Multicomponent transport model based on the Stefan-Maxwell theory and continuum mechanics
Jan Franců
FNSPE CTU in Prague
Sunday 12. 6. 2016, 10:50 – 11:10
Although the general equations had been proposed nearly 50 years ago, only recently the model
combining the Stefan-Maxwell theory of diffusion with equations of fluid flow has been brought
to light. In this contribution an elegant model for describing both convection and diffusion
of components in a multicomponent fluid mixture is presented. Its effectiveness is demonstrated
through a numerical analysis of simplified equations, which are solved using finite volume methods
(FVM).
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Multidimensional exact solution for two-phase flow in porous media
Radek Fučı́k
FNSPE CTU in Prague
Friday 10. 6. 2016, 14:00 – 14:30
In general, analytical solutions serve a useful purpose to obtain better insights and to verify
numerical codes. For flow of two incompressible and immiscible phases in homogeneous porous
media without gravity, one such method that neglects capillary pressure in the solution was
first developed by Buckley and Leverett (1942). Subsequently, McWhorter and Sunada (1990)
derived an exact solution for the one and two dimensional cases that factored in capillary effects.
This solution used a similarity transform that allowed to reduce the governing equations into
a single ordinary differential equation (ODE) that can be further integrated into an equivalent
integral equation. We present a revision to McWhorter and Sunada solution by extending the
self-similar solution into a general multidimensional space. Inspired by the derivation proposed
by McWhorter and Sunada (1990), we integrate the resulting ODE in the third and higher
dimensions into a new integral equation that can be subsequently solved iteratively by means
of numerical integration. We developed implementations of the iterative schemes for one- and
higher dimensional cases that can be accessed online on the authors’ website.
Template Numerical Library on Intel Xeon Phi
Vı́t Hanousek
FNSPE CTU in Prague
Sunday 12. 6. 2016, 11:30 – 11:55
This talk will shortly introduce the Intel Xeon Phi coprocessor and its offload programing model.
Then the current state of the Xeon Phi experimental support in the Template Numerical Library
will be presented. Possible optimization techniques for a performance improvement will be
discussed at the end of this talk.
Discontinuous Galerkin High-Order Nonlocal Transport and Energy Equations Scheme for Radiation-Hydrodynamics
Milan Holec
FNSPE CTU in Prague, Institute of Physics, AS CR, v.v.i
Sunday 12. 6. 2016, 09:30 – 09:55
The classical description of transport based on Chapman-Enskog approach has been always
widely used in fluid models thanks to its simplicity. Nevertheless, it has been shown that the
classical local approach is not accurate when the fluid parameters exhibit steep gradients, which
is the typical case of laser heated plasmas. An intensive effort has been made to model the
nonlocal radiative energy transport in radiation-hydrodynamics simulations in the last decades.
From the existing models we solve directly the photon transport equation allowing one to take
into account the effect of long-range photon transport. Our approach delivers a calculation
efficiency and an inherent coupling of radiation to the fluid plasma parameters in an implicit
way. The use of high-order discontinuous Galerkin method gives us an accurate solution to
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the transport, that obeys both limiting cases, i.e. the local diffusion asymptotic usually present
in radiation hydrodynamics models and the collisionless transport asymptotic of free-streaming
photons. In other words, we can analyze the radiation transport closure for the radiationhydrodynamics and how it behaves when leaving the conditions of validity of Chapman-Enskog
method. This is demonstrated numerically in the tests of the exact steady transport of any
regime and the approximate time-dependent multi-group diffusion of energy. As an application
we present simulation results of intense laser-target interaction, where the radiative energy
transport, controlled by the mean free path of photons, shows the importance of the nonlocal
model.
A numerical method for optical flow
Viera Kleinová, Peter Frolkovič
SvF STU, Bratislava
Saturday 11. 6. 2016, 09:30 – 10:00
Optical flow is today very important topic in medicine, computer vision and image processing.
The main goal is to determine optical flow based on level-set motion between two images. We
present preliminary results of our numerical method. Our illustrative examples include synthetic
and real data. Some representative results will be presented.
A massively parallel implementation of two-phase immiscible flow
in porous media using the mixed-hybrid finite element method
Jakub Klinkovský
FNSPE CTU in Prague
Friday 10. 6. 2016, 11:55 – 12:15
The work deals with a numerical solution of two-phase immiscible flow in porous media and
a massively parallel implementation of the model using the architecture of modern GPUs. We
devise a semi-implicit numerical scheme that is based on the mixed-hybrid finite element and
finite volume methods and stabilized using the upwind and mass-lumping methods. The scheme
is implemented for parallel GPU architectures using the CUDA platform and the TNL library.
The accuracy of the solver is verified by an experimental analysis of convergence
for benchmark problems with known semi-analytical solutions. For an advection-diffusion problem
in heterogeneous porous medium, various capillarity models and numerical scheme variations
are compared with a reference solution published in literature. The efficiency of the parallel
computation on GPU is analyzed in detail for a selected test problem.
Numerical Solution of Constrained Curvature Driven Flow
Miroslav Kolář
FNSPE CTU in Prague
Sunday 12. 6. 2016, 09:55 – 10:20
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We investigate the numerical solution of the evolution law for the constrained curvature flow for
open and closed curves in the plane. The model schematically reads as
normal velocity = curvature + force,
where the particular choice of the (possibly non-local) force term causes the structure-preserving
property. In this contribution, we study the area preserving curvature flow, which originates in
the theory of phase transitions for crystalline materials and originally describes the evolution of
closed embedded curves with constant enclosed area. However, it can be also shown that this
area preserving mechanism works for open curves with fixed endpoints as well.
The resulting motion law is treated by means of the parametric method, resulting in a system
of degenerate parabolic partial differential equations. Unlike other possible approaches as, e.g.,
the level set method or the phase field method, the advantage of the direct approach is in the
time efficiency and the ability to track the motion of open curves.
We solve the parametric equations numerically by means of the semi-implicit flowing finite volume
method. To enhance the numerical stability, we discuss the technique of tangential redistribution.
Several results of our qualitative and quantitative computational studies will be presented.
Multi-Material Remap for Staggered Arbitrary Lagrangian-Eulerian
(ALE) Methods
Milan Kuchařı́k, Mikhail Shashkov
FNSPE CTU in Prague, XCP-4, LANL
Thursday 9. 6. 2016, 14:05 – 14:35
For hydrodynamic simulations of problems containing strong fluid compressions or expansions
(such as simulations of laser-plasma interactions), Lagrangian methods employing a moving
computational mesh are usually used. The Arbitrary Lagrangian-Eulerian (ALE) method is a
successful approach preventing the mesh cells from numerical degeneracies. Such method typically consists of three steps: a Lagrangian solver, advancing the solution and the mesh in time;
a mesh rezoner, keeping the moving mesh smooth; and a remapper, interpolating the fluid quantities between the meshes. Here, we focus on the last part of the ALE algorithm, especially
on remapping of multi-material fluid quantities in the staggered discretization. In our remapping approach, all (both cell-centered and nodal) fluid quantities are remapped in a flux-form,
while paying a special attention to their conservation and bound-preservation. Properties of
our remapping method are demonstrated on a suite of selected hydrodynamic multi-material
examples.
Useful Discrete Approximations of Laplacian and Gradient
Jaromı́r Kukal, Michal Beneš
FNSPE CTU in Prague, FNSPE CTU in Prague
Thursday 9. 6. 2016, 14:35 – 15:05
Fourier and Laplace transforms were employed to develop novel difference scheme which is
useful for the solving of parabolic partial differential equations and their systems. The first
aim of scheme design is to develop such discrete approximation of Laplacian which has fixed
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accuracy order but has maximum possible radial order. When the grid is periodic, the coefficients
of adequate scheme can be pre-calculated using linear methods. Tables of Laplacian coefficients
are included for square, hexagonal, cubic and dodechedral grids. The second aim of scheme design
is to develop adequate discrete approximation of gradient operator which indirectly satisfies the
radial condition as follows. The gradiet operator has to generate Laplacian with maximum
possible radial order. Unfortunately, the unknown coefficients of discrete gradient formula are
roots of quadratic equation system. Finally, the tables of gradient coefficients are included for
several particular cases together with the first simulation results.
Applications of planar and space curve evolution
Jiřı́ Minarčı́k
FNSPE CTU in Prague
Friday 10. 6. 2016, 09:00 – 09:20
In this contribution, we examine the theory of evolving curves and explore their use in several
applications. We present a mathematical framework for describing curves in space which is a
combination of the parametric and implicit approach. The framework has been developed to
simulate the geodesic flow on stationary and moving surfaces. Both analytical and numerical
results of the method will be presented. Along with applications in image processing, we will
discuss the use of curves in modeling of the river channel centerline migration caused by the
meandering process.
Mean Field Lévy Flight as Integer Optimization Heuristics
Matej Mojzeš
FNSPE CTU in Prague
Thursday 9. 6. 2016, 15:05 – 15:30
Integer optimization heuristics are the only feasible option for a variety of NP-hard optimization problems that need to be solved in real-world conditions. Based on trial and error and
often enhanced by e.g. evolutionary, physical or biological processes they are able to find
or approximate global optimum on very large search spaces. The purpose of our research is
to contribute to family of heuristic method with a novel population based integer optimization
heuristic that yields from the theory of Mean Field Annealing. Population center and covariance
matrix are estimated for a given annealing temperature and then used as directional correction
of Lévy Flight mutation, which delivers reputable results in heuristic optimization. Inspired by
Competitive Differential Evolution, the proposed heuristic is of competitive nature with nine Lévy
Flight mutations competing together and being selected according to their success. The resulting heuristic has four parameters: population size, regularization factor, annealing temperature
and Lévy Flight temperature. Depending on the task complexity, there is relationship between
searching efficiency and regularization, annealing and heavy-tailed flights. Last, but not least,
performance of the novel method is demonstrated on benchmark Clerc’s Zebra3 and Hilbert matrix
inversion problems which are difficult tasks with many local extremes.
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TNL: FDM on GPU in C++
Tomáš Oberhuber
FNSPE CTU in Prague
Thursday 9. 6. 2016, 16:30 – 17:00
We present Template Numerical Library with native support of CUDA for computations on GPUs.
The library is written in C++ and it uses C++ templates extensively. The templated design of
TNL allows to develop solvers of PDEs with GPU support relatively easily and almost without
any knowledge of GPUs. The aim of TNL is to provide an easy to use tool for numerical
mathematicians so that they may concentrate only to numerical methods but they can still profit
from modern accelerators and parallel architectures. We will also discuss disadvantages of C++
templates and metaprogramming.
Numerical study of spiral motion and tip meandering
Petr Pauš, Shigetoshi Yazaki
FNSPE CTU in Prague, Meiji University, Tokyo
Thursday 9. 6. 2016, 17:00 – 17:30
The talk focuses on the numerical simulation of spiral motion which occurs for example during
Belousov-Zhabotinsky reaction. The spiral is simulated as an open parametric curve and approximated by the polygonal chain. The time evolution is based on the mean curvature flow equation.
Parametric approach allows for the detailed description of the force applied to the spiral tip.
The force consists of normal and tangential components which depend on several parameters
and can be changed independently. We performed simulations under various settings of the tip
force and studied the tip motion (meandering) in detail. The spiral motion is restricted to the
circular domain. To avoid the loss of accuracy and expansion of the spiral outside the domain,
we incorporated an algorithm which relocates the discretization points back to the computational
domain allowing long time computations with relatively small number of discretization points.
Numerical Computation of Two-Phase Compositional Flow in Porous
Media
Ondřej Polı́vka
FNSPE CTU in Prague
Friday 10. 6. 2016, 14:30 – 14:55
We deal with the numerical modeling of compressible multicomponent two-phase flow in porous
media with species transfer between the phases.
The mathematical model is formulated by means of the extended Darcy’s laws for all phases,
components continuity equations, constitutive relations, and appropriate initial and boundary
conditions. The splitting of components among the phases is described using a formulation of
the local thermodynamic equilibrium which uses volume, temperature, and moles as specification
variables.
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The problem is solved numerically using a combination of the mixed-hybrid finite element method
for the total flux discretization and the finite volume method for the discretization of continuity
equations. These methods ensure the local mass balance. The resulting system of nonlinear
algebraic equations is solved by the Newton-Raphson iterative method. The numerical flux is
discretized in a way that no phase identification nor determination of correspondence between
the phases on adjacent elements is required in contrast to the traditional approaches. This is
very important for the simulations of CO2 sequestration because, typically, the CO2 is injected
into a reservoir in the supercritical state at which the phase distinction is ambiguous. Moreover,
our model performs well in situations where a phase appears or disappears and no switching of
variables is needed.
We briefly describe the numerical method and provide several 2D simulations, e.g. CO2 injection
into water saturated reservoir.
Computation of equilibrium states at constant internal energy, volume and moles
Tomáš Smejkal
FNSPE CTU in Prague
Sunday 12. 6. 2016, 11:10 – 11:30
In this contribution, phase stability and phase equilibrium of multicomponent mixtures at given
internal energy, volume and moles will be discussed. We derive criterion for phase stability
and devise numerical algorithm based on Newton-Raphson method for testing phase stability.
We also devise a new algorithm for general p-phase equilibrium calculation, which is based on
the direct maximization of the total entropy of the mixture with respect to the internal energy-,
volume- and mole-balance constraints. We present the properties of the algorithms on several
examples of phase equilibrium calculations.
Quantification of trapped gas in dual-porosity media with continuous and discontinuous domains
Michal Sněhota, Jan Šácha, Jan Hovind
Friday 10. 6. 2016, 11:00 – 11:30
FCE CTU in Prague, University Centre for Energy Efficient Buildings, CTU in Prague and Paul
Scherrer Institut, Villigen, Switzerland
Nonwetting phase (residual air) is trapped in the porous media at water contents close to the
saturation. Trapped gas phase resides in pores in form of bubbles, blobs or clusters forming
residual gas saturation. In homogeneous soil media trapped gas is relatively stable until it is
released upon porous media drainage. If porous media remain saturated, trapped gas can slowly
dissolve in response to changed air solubility of surrounding water. In heterogeneous media,
relatively rapid change in the trapped gas distribution can be observed soon after the gas is
initially trapped during infiltration. It has been recently shown that the mass transfer of gas
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is directed from regions of fine porosity to regions of coarse porosity. The mass transfer was
quantified by means of neutron tomography for the case of dual porosity sample under steady
state flow. However the underlying mechanism of the gas mass transfer is still not clear. Based
on the robust experience of visualization of the flow within heterogeneous samples, it seems
that due to the huge local (microscopic) pressure gradients between contrasting pore radii the
portion of faster flowing water becomes attracted into small pores of high capillary pressure.
The process depends on the initial distribution of entrapped air which has to be considered
as random in dependence on the history and circumstances of wetting/drying. In this study,
the redistribution of trapped gas was quantitatively studied by 3D neutron imaging on samples
composed of fine porous ceramic and coarse sand. The redistribution of water was studied under
no-flow and steady state flow conditions. Two different inner geometries of the samples were
developed. In the first case the low permeability regions (ceramics) were disconnected, while in
the second structure, the fine porosity material was continuous from the top to the bottom of the
sample. Quantitative 3D neutron tomography imaging revealed similar redistribution process in
both cases of interconnected and disconnected fine pore systems. The rate of the redistribution
was significantly higher in the case of steady state flow condition in comparison to no-flow
conditions. The transfer from fine to large pores led to reduced hydraulic conductivity of the
sample.
Mathematical modeling of contaminant transport in porous media
Jakub Solovský
FNSPE CTU in Prague
Friday 10. 6. 2016, 12:15 – 12:35
This work deals with two phase compositional flow. We present equations describing two
phase flow, component transport and interphase mass transfer. For this type of problems, we
propose a numerical method based on the mixed hybrid finite element method. We implement
several variations of this method using different approaches to solving resulting system of linear
algebraic equations. We use direct and iterative solvers and parallel implementation using MPI.
The method is verified on problems for which exact solutions are known or solutions can be
found in literature. Numerical experiments show that the errors are similar for all variations
of the method. The method is convergent and the order of convergence is slightly less than
one. There are significant differences in the computational time. Iterative solvers are faster
and the parallelism is advantageous while using fine meshes. In the next part, we focus on the
compositional flow. Data from two experiments are used and numerical results are compared
with measured values.
The first experiment was focused on evaporation of dissolved TCE. For low air flow rates above
the water table, there is a good match with experimental data. For higher flow rates, the
results differs. The second, more complex experiment in larger scale examined the influence of
water table fluctuation and rainfall events on evaporation and transport of the dissolved TCE.
For water table fluctuation, there is a good match with experimental data but for rainfall events
there are significant differences. During the rainfall events there are uncertainties concerning
the experimental data. Differences between the measured values and the numerical simulations
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indicate certain limits of the mathematical model used or the influence of other processes that
are neglected in the current model. Finally we focus on hypothetical scenarios of vapor intrusion.
In the field scale, we examine effect of water table drop or rainfall events, that were in smaller
scale studied experimentally.
Numerical results are similar to the second experiment.
A Hybrid Parallel Numerical Algorithm for Three-Dimensional Phase
Field Modeling of Crystal Growth
Pavel Strachota
FNSPE CTU in Prague
Thursday 9. 6. 2016, 16:00 – 16:30
We introduce a hybrid parallel numerical algorithm for solving the phase field formulation of the
anisotropic crystal growth during solidification. The implementation is based on the MPI and
OpenMP standards. The algorithm has undergone a number of efficiency measurements and
parallel profiling scenarios. We compare the results for several variants of the algorithm and
decide on the most efficient solution.
A posteriori error estimates for finite element solutions of Poisson
equation
Vojtěch Straka
FNSPE, CTU in Prague
Friday 10. 6. 2016, 09:20 – 09:40
A wide variety of phenomena in physics and other sciences can be described by partial differential equations. In majority of cases, finding an analytical (exact) solution is not possible,
therefore numerical methods are applied as simulation tools. However, these methods typically
only deliver an approximate solution, which is different from the exact solution. For evaluation
of the error between the known numerical and the unknown exact solution, a posteriori error
estimates can be used.
In this presentation, a general introduction to a posteriori error estimation will be made. Then a
specific form of a posteriori estimates for Poisson equation will be discussed and finally numerical
results for model problems will be presented.
Lattice Boltzmann Method and Natural Convection
Robert Straka
AGH Krakow
Friday 10. 6. 2016, 09:40 – 10:10
The inclusion of a buoyant force into the LBM will be presented. Resulting macroscopic system
of equations describe the problem of natural convection i.e. when the flow is induced due to
density (temperature) gradients of given fluid. A good example is hot air movement above a
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heater. Multiple relaxation time (MRT) flavor of LBM together with Smagorinsky Subgrid Scale
(SGS) LES turbulence model is applied to solve the fluid motion, single relaxation time (SRT)
LBM for the second population of distribution functions, again with SGS LES is used to solve
an advection-diffusion equation for the temperature field. Application of the above model is then
applied to simulate heating of a room during the winter season. Dynamics of hot cold air for
different locations of the heater will be presented.
Two-stage Alpha-Stable Distribution Parameters Estimation Approach
Tran Quang Van
FNSPE CTU in Prague
Thursday 9. 6. 2016, 17:30 – 18:00
Financial asset returns tend to have heavier tail distribution than normal distribution and alpha
stable distribution may be a suitable candidate for capturing this characteristic feature of asset
returns. This heavy-tail distribution is characterized by four parameters which need to be
estimated. They can be estimated by numerical integration approach, but it might be time
consuming. We propose an approach based on maximum likelihood estimation method in which
the parameters of alpha stable distribution are estimated consequentially in two stages. At
the first stage two parameters alpha and beta are determined in an outer optimization loop
from the standardized alpha stable distribution pdf obtained by fast Fourier transform. After
that the remaining two parameters can be easily estimated in an inner optimization loop. The
applicability of this two-phase likelihood maximization estimation technique is then verified on
artificially simulated data alpha stably distributed and after that it is used to estimate parameters
of alpha stable distribution of actual stock market indices returns series.
Construction of upper bounds of the HOMO-LUMO spectral gaps
by semidefinite relaxation techniques
Daniel Ševčovič
Comenius University
Sunday 12. 6. 2016, 09:00 – 09:30
In computational chemistry, the spectral properties of graphs describing organic molecules play
an important role. The molecular orbital energy is associated with eigenvalues of the graph
representing the molecule. More precisely, given an invertible graph G of an organic molecule,
the energy of the highest occupied molecular orbital (HOMO) is related to the lowest positive
eigenvalue of the adjacency matrix of the graph, and the energy of the lowest unoccupied
molecular orbital (LUMO) corresponds to its largest negative eigenvalue. The so-called HOMOLUMO spectral gap of the graph is then defined as the difference of HOMO and LUMO eigenvalues
of the adjacency matrix of the structural graph of a molecule.
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The aim of this talk is to present computational methods for obtaining upper estimates on the
HOMO-LUMO spectral gap of graphs constructed from two prescribed structural graphs by
bridging over their vertices. The problem leads to a mixed integer semidefinite programming
problem which is an NP hard problem in general. We present a convex relaxation of the original
problem leading to a numerically tractable method for construction of the upper bound of the
HOMO-LUMO spectral gap.
Efficient point cloud registration using PCL library
Róbert Špir, Lenka Hrapková, Karol Mikula
SvF STU, Bratislava
Saturday 11. 6. 2016, 09:00 – 09:30
Laser scanning and point cloud representation is common method to obtain 3D models of various
objects or environments in medicine, architecture or digitalization of monuments and historical
memorabilia. The most common problem is alignment of multiple scans of the same object from
different angles to form single complete 3D model, especially when there is only small overlap
of scans. In this work we will present efficient and fast registration of multiple large point cloud
scans (more than 10 million points per scan) and their alignment using point-cloud library (PCL)
with custom parallelization of calculation steps.
Quantitative evaluation of water distribution from two and threedimensional neutron images the during ponded infiltration
Jan Šácha, Michal Sněhota, Jan Hovind
FCE CTU in Prague, Paul Scherrer Institute, Switzerland
Friday 10. 6. 2016, 11:30 – 11:55
Modern imaging techniques such as neutron imaging (NI) provide spatial and temporal information about the water and air distribution within the porous media. This information during
hydrological processes is important for evaluating current and developing new water transport
models. NI is characterized by relatively short acquisition times (seconds) and high resolution of
images (micrometers). The acquisition time increases with the better resolution and vice versa.
Depending on a research focus (static or dynamic processes) the choice of parameters is of a
high importance. At the same time, the appropriate data processing has to be applied to obtain
results free of bias and artifacts. Ponded infiltration experiments were conducted on two soil
samples packed into the quartz glass columns of inner diameter of 29 and 34 mm, respectively.
First sample was prepared by packing of fine and coarse fractions of sand and the second sample
was packed using coarse sand and disks of fine porous ceramic. Ponded infiltration experiments
conducted on both samples were monitored by neutron radiography to produce two dimensional
(2D radiograms) projection of images during the transient phase of infiltration. During the steady
state flow stage of experiments neutron tomography was utilized to obtain three-dimensional
(3D tomograms) information on gradual water redistribution. The acquired radiographic images
were normalized for background noise and spatial inhomogeneity of the detector, fluctuations of
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the neutron flux in time and for spatial inhomogeneity of the neutron beam. The radiograms of
dry sample were subtracted from all subsequent radiograms to determine water thickness in the
2D projection images.
All projections were corrected for beam hardening and neutron scattering by empirical method.
Parameters of the correction method uses were identified by fitting the volume of water in the
entire sample in given time (from radiograms) to gravimetrically determined amount of water
in the sample. The results from this correction is 2D water thickness maps of the sample.
Tomography images were reconstructed from corrected water thickness maps to obtain the 3D
spatial distribution of water content within the sample which can be compared with results of
mathematical models.
Modeling of Water-Ice Interface within Freezing Soil at MicroScale
Alexandr Žák
FNSPE CTU in Prague
Friday 10. 6. 2016, 15:40 – 16:10
This contribution deals with a 2D micro-scale model of thermomechanical processes during
solidification of a medium within porous material. The problem description is performed by
means of heat balance and momentum conservation within individual phases; the solidification
is traced using a phase-field equation. Suitable couplings of multi-phase and multi-physics are
introduced. Several computational results are
presented.
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Hiking excursion
This year we will have excursion to Pravčická brána. The Pravčická brána is a narrow rock
formation located in the Bohemian Switzerland in the Czech Republic. With a span of 26.5
metres, an inside height of 16 metres, 8 metre maximum width and 3 metre arch, it is the largest
natural sandstone arch in Europe, and one of the most striking natural monuments in the Elbe
Sandstone Mountains.
There will be a common departure from Dečı́n main square by bus on Saturday at 11:08. Let
us meet in front of the Zámecká sýpka (Castle grange) at 10:30. We will get off at Meznı́ Louka
and walk along the red hiking route. The trip is roughly 7 km long. The route is denoted by
a dashed black line in the map below. Tough guys can walk further to Hřensko along the red
hiking route (+3km) or even to Dečı́n (+20.5 km).
The departures of return buses:
From Meznı́ louka: 14:09, 16:09, 18:09, 20:09
From Pravčická brána: 14:14, 16:14, 18:14, 20:14
From Hřensko, nábřežı́: 14:23, 16:23, 18:23, 20:23
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