Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes

In this paper, certain well-known upwind schemes for hyperbolic equations are extended to solve the two-dimensional Saint-Venant (or shallow water) equations. We consider unstructured meshes and a new type of finite volume to obtain a suitable treatment of the boundary conditions. The source term involving the gradient of the depth is upwinded in a similar way as the flux terms. The resulting schemes are compared in terms of a conservation property. For the time discretization we consider both explicit and implicit schemes. Finally, we present the numerical results for tidal hows in the Pontevedra ria, Galicia, Spain. (C) 1998 Elsevier Science S.A.