A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System

A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36, 397-425, 2002. Depending on the reconstruction step, the second-order versions of the schemes there could be made either well-balanced or positivity preserving, but fail to satisfy both properties simultaneously.