A generalized finite difference method for the 2-D nonlinear shallow water equations
Abstract
In this paper, we propose a generalized finite difference method for two-dimensional non-linear shallow equations. The space discretization uses the staggered grid C of Arakawa. Beside the implicit-explicit factor theta, the time discretization involves a balance ratio alpha of the spatial nodes. The stability analysis takes account the size of the parameters. We discuss the stabilizing properties of the scheme and present some numerical experiments.