Extension of an explicit finite volume method to large time steps (CFL>1): application to shallow water flows

Abstract

In this work, the explicit first order upwind scheme is presented under a formalism that enables the extension of the methodology to large time steps. The number of cells in the stencil of the numerical scheme is related to the allowable size of the CFL number for numerical stability. It is shown how to increase both at the same time. The basic idea is proposed for a 1D scalar equation and extended to 1D and 2D non-linear systems with source terms. The importance of the kind of grid used is highlighted and the method is outlined for irregular grids. The good quality of the results is illustrated by means of several examples including shallow water flow test cases. The bed slope source terms are involved in the method through an upwind discretization. Copyright © 2005 John Wiley & Sons, Ltd.