Adapting a Mesh when Simulating Tsunami Waves

Abstract

The principles and methods of adapting an unstructured mesh to the distribution of ocean depths for long-wave models of tsunamis are described. It is shown that, in order to adequately reproduce tsunamis within the long-wave theory, the perturbation introduced in the model has to be smoothed or filtered to eliminate short-period components subject to phase dispersion. An explicit formula to calculate the cutoff period for a filter is proposed. The relative numerical efficiency of using unstructured meshes adapted to the distribution of ocean depths compared to regular meshes is estimated. It is shown that using unstructured meshes can ensure an increase in numerical efficiency by up to several thousand factors.