A modified Rusanov method for simulating two-layer shallow water flows with irregular topography

In the current paper, we develop and suggest a modified Rusanov method for simulating two-layer shallow water flows with variable topography. The coupling between two-layers results in a non-conservative product term which involves the partial derivatives of unidentified physical parameters, as a result, the model is conditional hyperbolic. The stages of this scheme are predictor and corrector. A parameter for managing the numerical diffusion is included in the predictor stage, which is accomplished through the use of limiters theory. The balance conservation equation is recovered by the corrector stage. To prove the efficacy of the suggested scheme, we offer a number of numerical tests. The numerical outcomes indicate how accurate and well-balanced the suggested method is for simulating two-layer shallow flows with irregular topography.