Well-balanced central schemes for two-dimensional systems of shallow water equations with wet and dry states

The aim of this paper is to develop a new second-order accurate central scheme for the numerical solution of the two-dimensional system of shallow water equations (SWE) featuring wet and dry states over variable waterbeds. The proposed central scheme follows a classical Riemann-free finite volume method and evolves the numerical solution of systems of hyperbolic balance laws on a single Cartesian grid. Furthermore, the proposed well-balanced scheme preserves the lake at rest constraint thanks to a careful well-balanced discretization of the SWE system, and allows a proper interaction between wet and dry states whenever water run-ups/drains arise. For verification purposes, classical SWE problems appearing in the recent literature are successfully solved.