Hardware Acceleration of Tsunami Wave Propagation Modeling in the Southern Part of Japan

Abstract

In order to speed up the calculation of tsunami wave propagation, the field-programmable gate array (FPGA) microchip is used. This makes it possible to achieve valuable performance gain with a modern regular personal computer. The two half-step MacCormack scheme was used herein for numerical approximation of the shallow water system. We studied the distribution of tsunami wave maximal heights along the coast of the southern part of Japan. In particular, the dependence of wave maximal heights on the particular tsunami source location was investigated. Synthetic 100 × 200 km sources have realistic parameters corresponding to this region. As observed numerically, only selected parts of the entire coast line are subject to dangerous tsunami wave amplitudes. The particular locations of such areas strongly depend on the location of the tsunami source. However, the extreme tsunami heights in some of those areas can be attributed to local bathymetry. The proposed hardware acceleration to compute tsunami wave propagation can be used for rapid (say, in a few minutes) tsunami wave danger evaluation for a particular village or industrial unit on the coast.

Algorithmic Design of an FPGA-Based Calculator for Fast Evaluation of Tsunami Wave Danger

“…H t + (uH) x + (vH) y = 0, u t + uu x + vu y + gH x = gD x v t + uv x + vv y + gH y = gD y , (1) where H(x,y,t) = η(x,y,t) + D(x,y) is the distance from the sea's surface to the bottom, η is the sea surface displacement relative to the mean sea level (wave height), D(x,y) is the water depth (which is supposed to be known at all grid points), u and v are the water flow velocity components in the x and y directions, respectively, and g is the gravity force acceleration. Note that the lower indices t, x, y in (1) indicate partial derivatives with respect to time and space variables.…”

“…Thus, the proposed approach was applied to the MacCormack scheme. As the result, a special processor element (PE) was designed to implement one step of the algorithm (see [1]). By composing PEs into a line, the calculator can be scaled to different FPGAs.…”

“…Since power supply outages are possible in the event of catastrophic earthquakes, it is important to be able to quickly receive and analyze the measured data received, regardless of the centralized power supply. The FPGA-based calculator previously proposed by the authors [1] makes it possible to fulfill both of these requirements, which usually contradict one another. The use of HLS technology can significantly reduce the porting time of the algorithms used to the proposed hardware platform.…”

Fast Modelling of Tsunami Wave Propagation using PC with Hardware Computer Code Acceleration

“…Calculator based of FPGA microchip Xilinx Virtex-7 VC709 was used for numerical tests (see [7,8] for details). Fig.…”

“…Alternatively, the Mac-Cormack scheme for numerical approximation of the shallow water equations was implemented [7,8]. Comparison with the exact solutions (in special cases of sea bed relief) shows a very good accuracy of the implemented method [9,10].…”