On the numerical modeling of tsunami wave generation and propagation

In this article three main stages of tsunami wave evolution are investigated. At first, the development of disturb­ances from a given patched elevation of the bottom surface in an incompressible nonviscous fluid of the uniform depth is consid­ered. Then, a tsunami wave diffraction by underwater bottom elevation or cavity is investigated. In this case the shallow water equations are already used, and it is supposed that a cylindrical wave is spread from patched water elevation over the epicentrum. Last, the tsunami propagation and transformation in a shallow water region and its run-up on a beach are investigated on the basis of the improved shallow water theory, taking into considera­tion the nonlinear and dispersive terms of higher order. The pro­posed theory is tested in a problem of collisions of two solutions. Solutions of the first and the second problems are obtained by the method of integral Laplace’s transformation with following nu­merical inversion of transformations. A finite difference method for a solution of the last problem is used.