An effect non-staggered central scheme based on new hydrostatic reconstruction

Abstract A non-staggered second-order accurate central scheme based on new hydrostatic reconstruction (HR) for the shallow water equation (SWE) with dry–wet fronts is presented. The well-balanced property maybe missed if the discretization of the source term based on an invariable water surface level on the staggered cell. We propose a novel discretization of the source term based on new hydrostatic reconstruction to ensure the well-balanced property on the staggered cell. To evolve the numerical solutions on a single grid and satisfy the well-balanced property, we construct a map between the water surface level and its cell average on the staggered cell. The positivity preserving property is achieved by providing an appropriate CFL condition. A number of classical problems for the SWE are successfully solved.

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