An improved technique for solving two-dimensional shallow water problems

Abstract

A numerical model for solving the 2D shallow water equations is proposed herewith. This model is based on a finite volume technique in a generalized co-ordinate system, coupled with a semi-implicit splitting algorithm in which a Helmholtz equation is used for the surface elevation. Several benchmark problems have proven the good accuracy of this method in complex geometries. Nevertheless, several numerical perturbations were noted in the surface elevation. After finding the origin, a new numerical technique is suggested, to avoid these perturbations. Several severe tests are proposed to validate this technique