The paper describes a new numerical algorithm that allows to simulate tsunami wave in a uniform manner throughout the entire its propagation zone, starting from the initial surface perturbation over the deepwater zone up to the shoreline, including the flooding and drying of a coastal zone. The algorithm is based on the regularized shallow water equations in conjunction with the adaptive choice of the regularization parameter. As an example, the tsunami wave propagation near the coast of Japan in 2011 is shown.
02.60.-x Numerical approximation and analysis
47.11.-j Computational methods in fluid dynamics
$^1$Keldysh Institute of Applied Mathematics RAS\
$^2$Faculty of Physics, M.V. Lomonosov Moscow State University.
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