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

Events of a seismic nature followed by catastrophic floods caused by tsunami waves (the incidence of which has increased in recent decades) have an important impact on the populations of littoral regions. On the coast of Japan and Kamchatka, it takes nearly 20 min for tsunami waves to approach the nearest dry land after an offshore seismic event. This paper addresses an important question of fast simulation of tsunami wave propagation by mapping the algorithms in use in field-programmable gate arrays (FPGAs) with the help of high-level synthesis (HLS). Wave propagation is described by the shallow water system, and for numerical treatment the MacCormack scheme is used. The MacCormack algorithm is a direct difference scheme at a three-point stencil of a "cross" type; it happens to be appropriate for FPGA-based parallel implementation. A specialized calculator was designed. The developed software was tested for precision and performance. Numerical tests computing wave fronts show very good agreement with the available exact solutions (for two particular cases of the sea bed topography) and with the reference code. As the result, it takes just 17.06 s to simulate 1600 s (3200 time steps) of the wave propagation using a 3000 x 3200 computation grid with a VC709 board. The step length of the computational grid was chosen to display the simulation results in sufficient detail along the coastline. At the same time, the size of data arrays should provide their free placement in the memory of FPGA chips. The rather high performance achieved shows that tsunami danger could be correctly evaluated in a few minutes after seismic events.