A Hybrid Second Order Scheme for Shallow Water Flows

We extend the well-balanced second order hybrid scheme developed in Donat and Martinez-Gavara (J. Sci. Comput., to appear) to the one-dimensional and two-dimensional shallow water system. We show that the scheme is exactly well-balanced for quiescent steady states, when a particular integration formula is employed, just as in the scalar models considered in Donat and Martinez-Gavara (J. Sci. Comput., to appear). A standard treatment of wet/dry fronts can easily be adapted, obtaining a robust scheme that produces well-resolved numerical solutions.