A well-balanced positivity-preserving multidimensional central scheme for shallow water equations

Abstract

Recently, an efficient and multidimensional central scheme has been proposed by applying the limiting process diagonally (Yan et al. (2023) [25]). The aforementioned approach is applied to solve the two-dimensional shallow water equations with non-flat bottom topography in this study. The nonnegativity of the updated water depth is preserved under a reasonable CFL condition. The well-balancedness is achieved by simply applying central difference discretization to the source term using the surface gradient method. The conservation of water mass is obtained by changing the scheme into conservation form. All the key features of the present scheme have been rigorously proven. Several numerical experiments are provided to illustrate the robustness of the proposed scheme, including simulations of shallow water equations with Manning's bottom friction and Coriolis forces.