An accurate finite volume method using fourth order Adams scheme on triangular grids for the Saint-Venant System

Abstract

In this study, a new finite volume method is developed for shallow water equations on a rotating frame. Most upwind methods, which perform well for gravity waves, lead to large oscillations and/or numerical damping for Rossby waves. We propose an upwind finite volume method on unstructured grids which provides accurate results both for Rossby and gravity waves. This method uses a high-order upwind scheme for the calculation of the numerical flux, and a fourth-order Adams method with an operator splitting approach for temporal integration. The Coriolis term is integrated analytically before and after solving the conservation law. The proposed method can successfully suppress the short-wave numerical noise without damping the long waves. The balance between the flux and Coriolis terms is preserved. This method presents more accurate results than some well-known upwind schemes.