# Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan
## 3 Numerical Results
### Numerical Results  
In this paper we checked the possibility of very rapid numerical simulation of tsunami wave propagation on a modern PC with FPGA-based acceleration. So, numerical simulation was performed  
Figure 4: The expected initial disturbance area for an M9 earthquake, according to [1]. Figure 5: A 3D image of the model tsunami source used for numerical modeling; see [5]. up to the depth of 10 m. Full reflection boundary conditions were used at this depth. At the parts of the boundary that separate our computational domain from the ocean, we used free passage of the wave out of the domain. To obtain detailed wave height maxima along the coast, in future we will use a nested grid approach with a mesh resolution of several meters at coastal areas. We began our study with the given shape of initial sea surface displacement at the tsunami source (see Figure 5). Then, the shape of the sea surface and components of the velocity vector were calculated according to shallow water Equation (1) in the entire water area under consideration. In Figure 6 is the distribution of the wave height maxima from the computed tsunami, generated by the model source _S0-c_ (cf. Figure 3). Figure 7a,b shows two frames of the time history of the free surfaces near the southwest of Shikoku Island as a result of the tsunami generated by source _S0-c_. In order to study the grid size sensitivity of the proposed method, the numerical experiment with source _S0-c_ was conducted on a new computational grid. In the coarse mesh, we used half the number of points in each direction. The numerical results are almost the same. Figure 8 shows the quantitative difference (in meters) between the distributions of wave maxima for these two cases over the entire computational domain. Almost everywhere, the difference between the wave height maxima does not exceed 0.2 m. Only near the coast, in the area opposite the source, this difference reaches almost 1 m.  
Figure 6: Calculated height maxima in the entire computational domain from a tsunami wave generated by source _S0-c_ (see Figure 3). Figure 7: Calculated tsunami heights near the southwest of Shikoku Island 1500 s (**a**) and 2000 s (**b**) after the start of propagation. In the left part of each picture, the color legend is presented. In the course of the computing experiments, the sources described in the previous section were located at close, intermediate, and distant positions relative to the coast in three locations near Shikoku Island and the Kii Peninsula shoreline. The most distant position of a source from the coast is the point near a deep-water trench axis (Figure 3). The results of numerical calculations in the form of the distributions of the wave height maxima are given in Figures 6 and 9, and Figure 10. The color scale in Figures 6 and 9, and Figure 10 shows the height-color relation for wave height values between 0 and 5 m. In cases where the tsunami height exceeds 5 m at certain grid points, we used for visualization the same color as the points with maximum level elevation of 5 m. Figure 6 shows the tsunami height maxima over the entire computational domain in the case of the most distant offshore source position at the south of Shikoku Island (model source _S0-c_). In Figure 9, the results for the closest source position just opposite the center of Shikoku Island are presented (source _S1-a_). Figure 10 shows the distribution of tsunami height maxima in the case of the intermediate tsunami source location near Kii Peninsula (source _S3-b_). The computational grid in use had 3000 \(\times\) 2496 nodes. According to our numerical results, the wave appears at the nearest dry land in 1000 s (approximately 16 min). The computation time to obtain the maximal wave height distribution in the entire water area is on the order of tens of seconds, provided that the proposed Calculator is applied to enhance the performance of a modern PC.