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

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 flows in the Pontevedra ria, Galicia, Spain.