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K. Kakuda et al.
5 Numerical Example
In this section, we present numerical results obtained from applications of the abovementioned approach to the dam-breaking fluid flow simulation. The initial velocities in
this problem are assumed to be zero everywhere in the interior domain. We set also the
gravity of 9.8 [m/s 2 ]. The fluid simulations are carried out on a 12 GB NVIDIA® Titan
V GPU and/or an Intel i9-7900X CPU with 64 GB memory, and the CNN & latent space
network are evaluated on a 11 GB NVIDIA® GeForce RTX 2080Ti GPU.
5.1 Dam-Breaking Fluid Flow Simulation
Table 1 gives the summary of the parameters for the dam-breaking fluid flow problem
with free surface. The fluid flow problem of broken dam includes many interesting
phenomena, namely large deformation of free-surfaces, very violent motions including
splashing, and so forth. The dam-breaking fluid flow problem has been extensively used
to verify the applicability and validity of the numerical methods. Figure 4 shows the
velocity fields at time step of 350 by using the autoencoder network (see Fig. 2(a)),
the reconstructed result with ELU and the present approach through comparison with
ground truth image. The loss time-history for the reconstructed velocity fields is shown in
Fig. 5. Our approach outperforms the latent space network with ELU activation function.
In Table 2, we present the comparison of the SPH simulation time and our CNN approach
time to get the velocities up to 12,500 time steps. We can see also from Table 2 that our
CNN performance leads to approximately 139 times speed-up.
Table 1. A summary of the parameters.
Tank area
Number of total particles
Number of fluid particles
Initial distance of two particles
Density
Viscosity coefficient
Surface tension coefficient
Time increment
8L×4L [m
2 ], L=0.146 [m]
11,171
8,756
0.00292 [m]
1000 [kg/m
3 ]
0.001 [Pas]
0.002361 [N/m]
0.0001 [s]
(a) Ground Truth
(b) Autoencoder
(c) Result using ELU
(d) Present
Fig. 4. Comparisons with ground truth for velocity fields at time step of 350.
K. Kakuda et al.
5 Numerical Example
In this section, we present numerical results obtained from applications of the abovementioned approach to the dam-breaking fluid flow simulation. The initial velocities in
this problem are assumed to be zero everywhere in the interior domain. We set also the
gravity of 9.8 [m/s 2 ]. The fluid simulations are carried out on a 12 GB NVIDIA® Titan
V GPU and/or an Intel i9-7900X CPU with 64 GB memory, and the CNN & latent space
network are evaluated on a 11 GB NVIDIA® GeForce RTX 2080Ti GPU.
5.1 Dam-Breaking Fluid Flow Simulation
Table 1 gives the summary of the parameters for the dam-breaking fluid flow problem
with free surface. The fluid flow problem of broken dam includes many interesting
phenomena, namely large deformation of free-surfaces, very violent motions including
splashing, and so forth. The dam-breaking fluid flow problem has been extensively used
to verify the applicability and validity of the numerical methods. Figure 4 shows the
velocity fields at time step of 350 by using the autoencoder network (see Fig. 2(a)),
the reconstructed result with ELU and the present approach through comparison with
ground truth image. The loss time-history for the reconstructed velocity fields is shown in
Fig. 5. Our approach outperforms the latent space network with ELU activation function.
In Table 2, we present the comparison of the SPH simulation time and our CNN approach
time to get the velocities up to 12,500 time steps. We can see also from Table 2 that our
CNN performance leads to approximately 139 times speed-up.
Table 1. A summary of the parameters.
Tank area
Number of total particles
Number of fluid particles
Initial distance of two particles
Density
Viscosity coefficient
Surface tension coefficient
Time increment
8L×4L [m
2 ], L=0.146 [m]
11,171
8,756
0.00292 [m]
1000 [kg/m
3 ]
0.001 [Pas]
0.002361 [N/m]
0.0001 [s]
(a) Ground Truth
(b) Autoencoder
(c) Result using ELU
(d) Present
Fig. 4. Comparisons with ground truth for velocity fields at time step of 350.