A Second Order Consistent MAC Scheme for the Shallow Water Equations on Non Uniform Grids

We propose in this paper a formally second order scheme for the numerical simulation of the shallow water equations in two space dimensions, based on the so-called Marker-And-Cell (MAC) staggered discretization on non uniform grids. For the space discretization, we use a MUSCL-like scheme for the convection operators while the pressure gadient is centered; time discretization is performed with the Heun scheme. The scheme preserves the positivity of the water height and “lake at rest” steady states. Its consistency in the Lax-Wendroff sense is proven.