Combining a Central Scheme with the Subtraction Method for Shallow Water Equations

We present a new numerical scheme that is a well-balanced and second-order accurate for systems of shallow water equations (SWEs) with variable bathymetry. We extend in this paper the subtraction method (resulting in well-balancing) to the case of unstaggered central finite volume methods that computes the numerical solution on a single grid. In addition, the proposed scheme avoids solving Riemann problems occurring at cell boundaries as it employs intermediately a layer of ghost-staggered cells. The proposed numerical scheme is then implemented and validated. We successfully manage to solve classical SWE problems from the literature featuring steady states and other equilibria. The results of the study are consistent with previous research, which supports the use of the proposed method to solve SWEs.