Calculation of storm surges and tsunamis via boundary‐fitted coordinates

Abstract

Two‐dimensional and three‐dimensional initial boundary‐value problems in an arbitrary domain are considered for the shallow‐water equations describing long‐wave disturbances of the sea surface. The problems are solved in curvilinear boundary‐fitted coordinates. In this connection the given domain is mapped onto a canonical one (e.g., a rectangle or a parallelepiped). A curvilinear grid in the given domain is mapped onto a rectangular grid in the canonical domain. The transformed equations are integrated on a regular grid by the finite‐difference method. For integration of the shallow‐water equations the semi‐implicit method with a nonrestrictive stability condition is used. The hybrid method used in the three‐dimensional case is based on the two‐dimensional realization for the level obtained by means of the integral velocity and the implicit scheme for finding the vertical distribution of velocity. Results of flood and tsunami calculations are presented.