A numerical algorithm for computing tsunami wave amplitude
Sergey Igorevich Kabanikhin1,2, Olga Igorevna Krivorotko1,2
1Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Lavrentieva, 6, Novosibirsk, 630090
2Novosibirsk State University, Pirogova 2, Novosibirsk, Russia, 630090
Keywords: уравнения мелкой воды, амплитуда фронта, фундаментальное решение, уравнение эйконала, конечно-разностный метод, shallow water equations, tsunami amplitude, fundamental solution, eikonal equation, finite difference approach
Abstract
A numerical algorithm for computing tsunami wave front amplitude is proposed. The first step consists in solving an appropriate eikonal equation. The eikonal equation is solved by the Godunov approach and the bicharacteristic method. The qualitative comparison of the two above methods is described. Then a change in variables associated with the eikonal solution is introduced. At the last step, using the expansion of the fundamental solution of shallow water equations in the sum of singular and regular parts, we obtain the Cauchy problem for the wave amplitude. This approach allows one to reduce computer costs. The numerical results are presented.
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