study of the overtopping flow impacts on multifunctional sea dikes in

E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
STUDY OF THE OVERTOPPING FLOW IMPACTS ON MULTIFUNCTIONAL SEA DIKES IN SHALLOW
FORESHORES WITH AN HYBRID NUMERICAL MODEL
CORRADO ALTOMARE
(1),(2)
(3)
(1)
(3)
(1),(6)
& TOMOHIRO SUZUKI
Ghent University, Ghent, Belgium,
[email protected]
School of Engineering, Hokkaido University, Hokkaido, Japan,
[email protected]
Department of Hydraulic Engineering, Delft University of Technology, Delft, The Netherlands,
[email protected]
(5)
(6)
(5)
Flanders Hydraulics Research, Antwerp, Belgium,
[email protected]
(2)
(4)
(4)
, YUKI OSHIMA , XUEXUE CHEN , ALEJANDRO J.C. CRESPO
Environmental Physics Laboratory, Vigo University, Ourense, Spain,
[email protected]
Department of Hydraulic Engineering, Delft University of Technology, Delft, The Netherlands,
[email protected], [email protected]
ABSTRACT
The present work describes the validation of a hybridization technique between two different numerical models, namely
SWASH and DualSPHysics, to study the impact of overtopping flows on multifunctional sea dikes in shallow foreshores.
Previous works on the SWASH-DualSPHysics hybridization were presented by Dominguez et al. (2014) and Altomare et
al. (2014), where the technique was validated against physical model results of wave propagation and run-up over sandy
beaches. The present work aims to extend the use of this hybridized model to the analysis of wave-structure interaction: a
typical case from the Belgian and Dutch coastline is used, where a building is constructed on the top of the dike. The
building represents the last defense against the overtopping flows and the wave loads acting on it have to be properly
characterized. Physical model tests were carried out at Flanders Hydraulics Research to measure forces on the vertical
wall (i.e. building), the layer thickness and velocities of the overtopping flows. The results from the experimental campaign
have been used to validate the hybridization. SWASH is previously validated against the physical model results: wave
propagation, transformation and breaking have been accurately modelled and the conditions at the toe of the dike are
reproduced as in the physical model test. Then SWASH is implemented together with DualSPHysics to model the wave
impact. A hybridization point along the physical domain has been defined. SWASH provides the boundary conditions for
DualSPHysics at that location. DualSPHysics is used to model the closest part of the domain to the dike. The results of
this hybridization strategy confirm the accuracy of the technique. Water surface elevation, velocity field of the overtopping
flows and wave forces, as measured in DualSPHysics, are in good agreement with the physical data. The results of the
validation are reported in this work.
Keywords: SPH, SWASH, hybridization, overtopping, wave loading
1.
INTRODUCTION
Multi-functional sea dikes are defense structures integrated with other social and public functions against coastal flooding
in low-lying countries, such as Belgium and the Netherlands. In the most common cases, there are buildings constructed
on the top of the dike. Wave overtopping is a major concern of dike safety in this study. During extreme conditions, long
waves would be generated on the shallow foreshore and bring severe overtopping water on the dike. If no further
countermeasures are implemented to cope with overtopping flows, the buildings are going to be the last defense against
such events, so they can be considered as part of the same coastal defense. Therefore, it is required to verify the overall
stability of the buildings against overtopping flow impacts and the local damages caused by overtopping waves on the
weakest parts of the construction. However, there is still lack of an assessment tool for this integrated coastal defense.
Some studies on overtopping in a shallow water condition and wave forces can be found in literature (e.g., Van Gent,
2002; Ramdsden, 1996), but the study of forces induced by overtopping flow is still limited. Physical model tests or
numerical models are therefore employed to characterize the overtopping flows and the wave-structure interaction for
multi-functional sea dikes in shallow foreshores. However physical modelling is often a costly and time-consuming
solution. Numerical approach is a possible alternative but modelling the whole processes from wave propagation in deep
ocean to the impact of overtopping flow on the dike is still a challenge within a single model due to the different and
multiple scales (both in space and in time) of the involved phenomena. Therefore, one single numerical model cannot be
only used to give reliable results.
To overcome this limitation, a hybridization technique is used in this study, which aims to couple two numerical models for
different physical processes, e.g., one is modelling the propagation of waves from offshore to coastline and the other is for
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
the wave-structure interaction. The two candidate models selected to perform this technique are SWASH and
DualSPHysics model.
The Simulating WAve till Shore (SWASH) model is a time domain model for simulating non-hydrostatic, free-surface and
rotational flow. Wave propagation models as SWASH (Zijlema et al., 2011) have been proven to be able to simulate
accurately surface wave and velocity field from deep water and with satisfactory results both in the open ocean and in
nearshore but they are not suitable to deal with coastal structures with an arbitrary shape such as a parapet since it is a
depth integrated model.
DualSPHysics is an open-source code based on the Smoothed Particle Hydrodynamics (SPH) method and can be freely
downloaded from www.dual.sphysics.org. The code DualSPHysics (Crespo et al. 2015) has been developed starting from
the SPH formulation implemented in SPHysics model. This SPH-based model has been used to study the wave
transformation and breaking at detailed scale close to the shoreline. SPH model is used to simulate free-surface flow
problems such as dam breaks, landslides, sloshing in tanks and wave impacts on structures (e.g. Lee et al., 2010;
Delorme et al., 2009). The expensive computational cost of SPH in comparison with other mesh-free methods for CFD
problems can be partially reduced by general-purpose graphics processing unit (GPGPU) where a Graphics Processing
Unit (GPU card) is used to perform computations traditionally managed by big cluster machines with thousands of CPU
cores. Notwithstanding, this is not enough if the goal is very demanding and if the purpose is to run the whole domain and
for the whole duration of storm events.
Previous works on the SWASH-DualSPHysics hybridization were presented by Domínguez et al. (2014) and Altomare et
al. (2014), where the technique was validated against physical model results of wave propagation and run-up over sandy
beaches.
The hybridization in general aims to overcome the limitations of the two models, using each model for a specific purpose
that best matches with its own capabilities. The advantages of using a hybridization technique between SWASH and
DualSPHysics can be summarized as follows:
•
Fast computations with large domains can be performed with SWASH, avoiding the simulation of large domains
with DualSPHysics that would requires huge computation times even using hardware acceleration.
•
SWASH is suitable for calculation where statistical analysis is necessary such as computing wave height and
good accuracy is obtained for wave propagation, whereas a certain wave decay is observed with standard SPH
formulation for large domains.
•
SWASH is not suitable for calculation of wave impacts on an arbitrary shape structure e.g parapet, while
DualSPHysics can easily compute wave impacts, pressure load and exerted force onto coastal structures
(Barreiro et al., 2013; Altomare et al., 2015).
•
Computation stability problems may appear in SWASH when a dry-wet condition is extensively used (e.g. 3D
overtopping flow calculation in complex geometries with some abrupt changes of the bathymetry). SPH in general
does not have such instability of the computation for any complex geometry or varying bathymetry.
The present work extends the application of the hybridization technique to model the impact of wave overtopping flows on
coastal structures. The main objective is to prove that overtopping flow characteristics (e.g. layer thickness, velocities) and
wave forces are correctly modelled and that the hybridization can represent a reliable solution to be used as
complementary or alternative to physical modelling.
2.
CASE OF STUDY
Physical model tests were conducted in a 4.0 m wide, 1.4 m deep and 70.0 m long wave flume at Flanders Hydraulic
Research, Antwerp, Belgium. A piston-type wave generator with a stroke length of 0.6 m was used to generate
monochromatic waves, without an active wave absorption system. The wave flume was split into four sections (1.0 m for
each), as shown in Figure 1. One reason of this design was to test the configurations with and without a wall
simultaneously (in order respectively to measure wave loading and overtopping rates). The other reason was to reduce
reflected waves by installing passive wave absorption baffles in the outer sections. Furthermore, by limiting the time series
of each experiment to the traveling time of the reflected waves towards the wave generator, the reflection would not affect
the measurements. Incident wave conditions were determined by measuring the waves without a dike in the outer section
(Fig. 1b): this approach is also used by Van Gent (1999) to obtain the incident wave properties (wave height and period)
and it is preferred compared to classical wave reflection analysis (Mansard and Funke, 1980) which cannot deal with
highly non-linear wave case. In the present case non-linear effects are dominating because of the very shallow foreshore.
The unobstructed overtopping flow features along the dike crest were measured in section A (Figure 1c) and section B
was used to measure the impact force of overtopping flow (Figure 1d). The overtopping flow was collected by an
overtopping tank behind the dike model in section A. The shallow foreshore profile was made in concrete, the dike models
consist of wooden plates. The main parameters are also depicted in Figure 1. The foreshore slope was 1:35 and dike
height 0.1 m. The dike slope used for the present work was 1:3. Further details on the experimental setup and physical
model results are reported in Chen et al. (2015). Only tests with regular wave trains have been used for this work.
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E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
Figure 1. Wave flume at Flanders Hydraulic Research (Antwerp, Belgium). (a) is a top view of the flume; (b), (c) and (d) are the respective
sections: outer section, A and B (source: Chen et al., 2015).
3.
NUMERICAL MODELS
3.1 SWASH model
The SWASH model is a time domain model for simulating non-hydrostatic, free-surface and rotational flow. The governing
equations are the shallow water equations including a non-hydrostatic pressure term. The SWASH model uses sigma
coordinates in the vertical direction and the number of the fluid layer can be changed in the calculation. By introducing the
layers, SWASH can maintain frequency dispersion even in a deep water condition. A full description of the numerical
model, boundary conditions, numerical scheme and applications are given in Zijlema et al. (2011).
Suzuki et al. (2011) demonstrated that this model produces satisfactory results for both wave transformation and wave
overtopping for shallow foreshore topography using one layer in their one-dimensional calculation. This numerical model is
a strong tool for the estimation of wave transformation since it is not demanding in terms of computation resources due to
the depth averaged assumption and parallel computation capability even though it is a time-domain model.
3.2 DualSPHysics model
DualSPHysics is a numerical model based on the Smoothed Particle Hydrodynamics (SPH) method (Crespo et al., 2015).
SPH is a Lagrangian and meshless method where the fluid is discretized into a set of particles and each of these particles
are nodal points where physical quantities (e.g. position, velocity, density, pressure) are computed as an interpolation of
the values of the neighboring particles. The contribution of the nearest particles is weighted according to distance between
particles and a kernel function (W) is used to measure this contribution depending on the interaction distance that is
defining using a smoothing length (h).
The mathematical fundamental of SPH is based on integral interpolants, therefore any function F can be computed by the
integral approximation. This function F can be expressed in a discrete form based on the particles. Thus, the
approximation of the function is interpolated at particle a and the summation is performed over all the particles within the
region of compact support of the kernel:
F (r )   F (r' )W (r  r ' , h )dr '
F (ra )   F (rb )W (ra  rb , h)
b
mb
b
[1]
[2]
where the volume associated to the neighboring particle b is mb/ρb, with m and ρ being the mass and the density,
respectively.
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The kernel functions W must fulfil several properties (Monaghan, 1992), such as positivity inside the area of interaction,
compact support, normalization and monotonically decreasing with distance. One option is a quintic kernel where the
weighting function vanishes for inter-particle distances greater than 2h.
In the classical SPH formulation, the Navier-Stokes equations are solved and the fluid is treated as weakly compressible
(e.g. see Gómez-Gesteira et al., 2012). The conservation laws of continuum fluid dynamics, in the form of differential
equations, are transformed into their particle forms by the use of the kernel functions.
The momentum equation proposed by Monaghan (1992) has been used to determine the acceleration of a particle (a) as
the result of the particle interaction with its neighbours (particles b):
P

d va
P
  mb  b2  a2  Π ab   aWab  g
dt
b
 ρb ρa

[3]
being v velocity, P pressure, ρ density, m mass, g=(0,0,-9.81) ms-2 the gravitational acceleration and Wab the kernel
function that depends on the distance between particle a and b. Πab is the viscous term according to the artificial viscosity
proposed in Monaghan (1992).
The mass of each particle is constant, so that changes in fluid density are computed by solving the conservation of mass
or continuity equation in SPH form:
dρa
  mb v ab   aW
dt
b
[4]
In the weakly compressible approach, the fluid is treated as weakly compressible and Tait’s equation of state is used to
determine fluid pressure based on particle density. The compressibility is adjusted so that the speed of sound can be
artificially lowered; this means that the size of time step taken at any one moment (which is determined according to a
Courant condition, based on the currently calculated speed of sound for all particles) can be maintained at a reasonable
value. Such adjustment however, restricts the sound speed to be at least ten times faster than the maximum fluid velocity,
keeping density variations to within less than 1%, and therefore not introducing major deviations from an incompressible
approach. Following Batchelor (1974), the relationship between pressure and density follows the expression
 ρ
P  B 
 ρ0
γ


  1


c02  0
B

where
[5]
[6]
  7 , and  0  1000 kg m -3 is the reference density.
The speed of sound co is defined at the reference density as
c o  c  ρo  
P
ρ
[7]
ρo
and it is numerically computed like at least 10 times the maximum velocity in the system that is determined as the wavefront velocity of a dam-break:
co  coef sound  g  hswl
[8]
being hswl the still water level and coefsound =10. The value of coefsound can be increased so compressibility of the fluid is
decreased according to Equations 5-6. Results using different values of coefsound will be discussed in next sections.
The Symplectic time integration algorithm (Leimkuhler, 1996) was used in the present work and a variable time step was
calculated, involving the CFL (Courant-Friedrich-Lewy) condition, the force terms and the viscous diffusion term.
DualSPHysics is capable of using the parallel processing power of either CPUs and/or GPUs making the study of real
engineering problems possible. Crespo et al. (2011) validated numerical results with experimental data in order to show
how the technique combines the accuracy and the efficiency of GPU programming. Thus, this new technology makes the
study of real-life engineering problems possible at a reasonable computational cost on a personal computer such as the
numerical design of coastal defenses with SPH models (Altomare et al., 2014; Altomare et al., 2015).
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E-proceedings of the 36th IAHR World Congress
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4.
THE HYBRIDIZED MODEL
The hybridization between DualSPHysics and SWASH has been obtained through a one-way hybridization at this stage.
The basic idea is to run SWASH for the biggest part of the physical domain to impose some boundary conditions on a
fictitious wall placed between both media. This fictitious wall acts as a non-conventional wave generator in DualSPHysics:
each boundary particle that forms the wall (hereafter called moving boundary or MB) will experience a different movement
to mimic the effect of the incoming waves. SWASH provides velocity values in different levels of depth. These values are
used to move the MB particles. The displacement of each particle can be calculated using a lineal interpolation of velocity
in the vertical position of the particle. Therefore the MB is a set of boundary particles whose displacement is imposed by
the waves that are propagated by SWASH but the MB only exists for DualSPHysics. A multi-layer approach (8 layers) has
been used in SWASH because it was previously proved to provide accurate results (Domínguez et al., 2014; Altomare et
al., 2014). The velocity has been interpolated and converted into displacement time series for DualSPHysics (Figure 2).
Figure 2. Scheme of multi-layer approach
All the details on the implementation of the hybridization technique between SWASH and DualSPHysics can be found in
Domínguez et al. (2014) and Altomare et al. (2014). A scheme of the application of the hybridization to the present case of
study is depicted in Figure 3. The hybridization section (hereafter defined also as “coupling point”) is located somewhere
over the foreshore slope. SWASH covers the domain from the physical wave paddle to the coupling point, meanwhile
DualSPHysics is used in a region where the dike or coastal structure is located.
5.
RESULTS OF THE HYBRIDIZATION
The results from the hybridization have been compared with the physical ones. The quantities to be measured and
compared are:
1.
water surface elevation after the coupling point (measured in the physical model by means of resistive wave
gauges);
2.
overtopping flow thickness in 3 different locations along the dike crest (measured in the physical model by means
of resistive wave gauges);
3.
overtopping flow velocity in an area close to the vertical wall (measured in the physical model using a BIV
technique in order to study the velocity patterns of the flows that are crashing and running over the wall);
4.
wave forces on the vertical wall (measured in the physical model by means of two-load cells of model series
Tedea-Huntleigh 614).
5.1 Preliminary results for hybridization point at x=30.24 m
Initially, the coupling point to hybridize SWASH and DualSPHysics has been chosen at a distance from the physical wave
paddle equal to 30.24 m because this location corresponds to the position of one of the resistive wave gauges located in
the physical flume at Flanders Hydraulics Research. On one hand, larger distances were considered to give inaccurate
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E-proceedings of the 36th IAHR World Congress,
28 June – 3 July, 2015, The Hague, the Netherlands
results because of the high wave breaking occurring on the foreshore, on the other hand smaller distances would have led
to a larger DualSPHysics domain with consequent increase of the computational cost. Later, the location of the coupling
point is discussed. The location of 30.24 m was used to investigate the sensitivity of the modelling with respect to proper
parameters of DualSPHysics model. This study helped to define the best numerical setup of DualSPHysics. A scheme of
the numerical model is represented in Figure 3: the wave height is measured at WG3, meanwhile the layer thickness is
computed in three positions on top of the dike (WG7, WG8 and WG9); the velocity field is measured in the green area in
the figure; the wave forces on the wall are calculated on the seaward face of the wall (in orange). At the top-left of the
figure, a sketch of the entire physical flume (measures not in scale) is represented with the definition of the domains where
SWASH and DualSPHysics have been used.
Figure 3. Sketch of the numerical model with indication of the coupling point and measurement locations
5.1.1 Sensitivity analysis of SPH parameters
The sensitivity analysis has been focused on three parameters that are characteristic of SPH model. The description and
the physical meaning of each of these parameter are explained as follows:
1.
2.
3.
Coefficient of sound, coefsound, is used to calculate the speed of sound, co, using Equation 8. Higher values of the
coefficient of sound means higher speed of sound values, hence less compressible fluid.
Coefficient of the artificial viscosity, α (for further details, see Monaghan, 1992). This parameter introduces an
artificial viscosity to stabilize the numerical noise and needs to be tuned in order to introduce the proper
dissipation.
Smoothing length coefficient, kh, is used to calculate the smoothing length, h, starting from the initial particle size
(dp) as h  k h  2 dp in 2D. The smoothing length defines the radius of interaction between particles. Larger
the smoothing length is, more neighbor particles are included in the iteration step for each fluid particle. However,
a very large smoothing length might increase unrealistic effects from the boundary particles (e.g. flume bottom)
on the behavior of the fluid ones. Thus, fluid particles on the free surface might “feel” the bottom such as a sort of
friction (see Figure 4).
Figure 4. Sketch of the influence of different smoothing lengths: the blue particle is interacting with the neighbors (in red) and with the
bottom based on the radius of interaction.
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E-proceedings of the 36th IAHR World Congress
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An initial particle size dp of 0.003m has been used, resulting in about 800,000 fluid particles. The simulation took 14.2h in
a GPU GeForce GTX680 to simulate 75s of physical time.
The results of the sensitivity analysis for wave forces, layer thickness and mean wave height are summarized in Table 1.
The wave height has been calculated by means of zero-crossing analysis of the water surface elevation. The velocity field
has been also compared with Chen et al. (2014) however is not included in the present paper. It is clear that smaller
values of the viscosity coefficient led to more accurate results both in wave forces and layer thickness. The analysis of the
coefficient of sound shows that the best results are achieved for values of 20. No significant differences are noticed
changing the smoothing length coefficient. The overall analysis of the results (including the comparison of the flow
velocities, not presented here) suggested to use the following setup for further calculations: coefsound=20, α=0.01, kh=1.5.
In general larger errors in the force estimation can be noticed than in the layer thickness and mean wave height. It can be
mentioned the fact that wave impact on coastal structures are very stochastic processes with poor repeatability: even
reproducing the same time series at the physical wave paddle, some differences in the force time series can be noticed
especially for impact loading or highly breaking processes. Furthermore, load cells are used in the physical model to
measure forces: the stiffness of the load cells and of the entire measurement setup might influence the signal that finally is
acquired and is, without any doubt, different by the “numerical force measurement”.
The first incoming wave has been excluded from the analysis because it is unrealistic and the assessment of forces and
layer thickness has been focused on the following three impact events. An example of the comparison of layer thickness
and wave forces between physical and numerical modelling is shown in Figure 5 and Figure 6.
Table 1. Sensitivity analysis results with coupling point at x=30.24 m
Coefficient of
sound
Viscosity
(α)
kh
Error [%]
10
0.01
1.5
Forces
(average 3 peaks)
30.3
16
0.01
1.5
48.6
40.1
27.0
20
0.01
1.5
33.0
18.4
25
0.01
1.5
35.2
22.7
30
0.01
1.5
38.4
19.2
Coefficient of
sound
Viscosity
(α)
kh
H (WG3)
6.7
23.1
7.2
11.6
8.6
9.4
17.7
21.4
4.9
23.3
19.2
6.2
Error [%]
0.01
1.5
Forces
(average 3 peaks)
33.0
20
0.05
1.5
37.2
Coefficient of
sound
Viscosity
(α)
kh
20
Layer thickness
(WG7, WG8, WG9)
42.0
36.0
36.9
Layer thickness
(WG7, WG8, WG9)
18.4
11.6
19.9
13.9
H (WG3)
8.6
9.4
16.0
2.5
Error [%]
Forces
(average 3 peaks)
Layer thickness
(WG7, WG8, WG9)
H (WG3)
20
0.01
0.9
31.1
12.9
11.9
21.1
1.0
20
0.01
1
33.0
22.6
12.3
16.7
3.7
20
0.01
1.5
33.0
18.4
11.6
8.6
9.4
Figure 5. Overtopping layer thickness at WG7, WG8 and WG9: comparison between numerical and experimental results.
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Figure 6. Wave forces (case with coefsound=20, α=0.01, kh=1.5): comparison between numerical and experimental results.
5.2 Identification of candidate hybridization points
SWASH has been used to model the wave propagation and transformation over the entire domain, where only the sea
dike was removed. Hence, the foreshore slope up to the toe of the dike has been modeled. The numerical flume
resembled the physical setup as in Figure 1 (b). The aim was to identify the region along the flume where the waves start
to break. Due to shoaling effects, the waves propagating along the flume start to become steeper and steeper (the wave
height increases with some decreasing in the wave period) until they reach a breaking condition (in shallow waters usually
depending on the water depth relative to the wave height). After breaking, a drastic reduction in the wave height can be
noticed. Hence, plotting the evolution of the significant wave height along the flume, it is easy to distinguish the point or the
area where the waves start to break (indicated by the vertical line in Figure 7). For the selected case of study, the breaking
point can be estimated at about 35.5 m. It is expected that coupling points after the breaking area would give worse results
than coupling points located before the breaking area.
Wave breaking point (=35.5 m)
Figure 7. Wave transformation and identification of the breaking point
The results from different coupling points are reported in Table 2 and shown in Figure 8 and the error in wave forces and
layer thickness with respect to the physical model results is reported. The run time for each case is also shown (Figure 9).
A case with the whole physical domain modelled in DualSPHysics is also reported: in such case the moving boundary is
represented by the physical wave generator and its location is then at x=0.00m. This case has been assumed as
reference case to measure the speedup of the calculation achieved with the SWASH-DualSPHysics hybridization (see last
column of Table 2). The run time to execute SWASH is not considered because it is about 3-5 min in a common personal
computer.
As expected, the accuracy of the hybridization modelling starts to decrease when the coupling point is just close or after
the breaking point. In average, the accuracy increases from x=0.00m to 30.24m, where the simulation is running already
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6.9 times faster than using only DualSPHysics for the entire domain. Therefore, the area between x=25.25 and 30.24 has
been identified as potential area to define the coupling point between SWASH and DualSPHysics.
Table 2. Comparison among different coupling point results (Errors in %), run times and speedups with respect to a full-domain simulation
in DualSPHysics.
Error [%]
Moving boundary location
Forces
[m] from the physical piston
(average 3 peaks)
WG7
Layer thickness
WG8
WG9
Run time
[h]
Speedup
0.00
25.60
23.90
30.20
17.70
97.40
---
20.25
42.60
12.90
9.30
17.30
40.00
2.4
25.25
33.30
18.90
15.70
17.50
25.20
3.9
30.24
33.00
18.40
11.60
8.60
14.20
6.9
32.25
57.90
30.30
24.10
30.70
13.90
7.0
33.25
61.80
15.70
27.10
32.60
11.20
8.7
35.25
57.10
34.10
33.60
32.70
8.90
10.9
38.25
91.40
46.90
54.40
71.00
5.50
17.7
Figure 8. Errors [%] for different coupling points.
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Figure 9. Run time vs distance of the coupling points from the physical wave generator.
6.
CONCLUSIONS
The present work introduces the first application of the hybridization technique between SWASH and DualSPHysics
models to wave impacts on coastal defenses. The case of study is a multi-functional sea dike in very shallow foreshore as
typical case of coastal defenses from Belgium and The Netherlands.
The hybridization technique has been validated against physical model results presented by Chen et al. (2014). A
sensitivity analysis has been conducted on certain parameters proper of the DualSPHysics modelling. Due to the
presence of shallow foreshore, the waves are heavily breaking before reaching the structure. The breaking point where
the waves start to break has been identified using only SWASH. Several simulations with coupling point in different
positions have been performed: as expected, the accuracy of the modelling decreases when the coupling point is located
close or after the breaking point. This analysis has shown that a good compromise between accuracy and run time is
found when the coupling point is located at a position between 25.25m and 30.24m far from the physical wave generator.
This distance corresponds to the 60% of the physical domain modeled only by using SWASH: therefore the last 40% is the
part of the domain where DualSPHysics is running. It has to be noticed that a change in the foreshore slope or in the water
depth might influence the breaking process and the location of breaking point along the domain: hence the position of the
coupling point and the percentage of the domain covered by each numerical model can be different from the present case.
The present study demonstrates that the hybridization technique between SWASH and DualSPHysics is a suitable
alternative to model phenomena of wave-structure interaction and wave impact on coastal defenses. Notwithstanding, this
study represents the first preliminary attempt to cope with wave impact on coastal structure in shallow foreshore condition.
Further research is already ongoing to improve the modelling results (e.g. introducing a 2-way hybridization).
10
E-proceedings of the 36th IAHR World Congress
28 June – 3 July, 2015, The Hague, the Netherlands
ACKNOWLEDGMENTS
The authors gratefully acknowledge the technical staff of Flanders Hydraulics Research and hydraulic laboratory of
Delft University of Technology for their great assistance to conduct the experiments. The present work is sponsored
by STW-programme on integral and sustainable design of multifunctional flood defenses, Project No. 12760 Flanders
Hydraulic Research, and the WTI 2017 project (Research and development of safety assessment tools of Dutch flood
defences), commissioned by the Department WVL of Rijkswaterstaat in the Netherlands. The second author (Yuki
Oshima) was supported by a scholarship awarded by the Engineering School of Hokkaido University. The financial
supports are gratefully acknowledged.
.
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