Abstract
Abstract In this paper, we propose an accurate Riemann-solver free method for a coupled system modeling shallow water flows, sediment transport and rapid bed erosion. The hydrodynamic model solving shallow water equations (SWEs) is coupled with the sediment transport equation and the morphodynamic model. A Godunov-type central-upwind scheme is proposed to numerically solve the resulting system based on the technique that using two different pairs of local wave speeds to estimate numerical fluxes for hydrodynamic and morphodynamic models, respectively. The proposed technique leads to accurate results for the computation of the morphodynamic model. The proposed scheme is based on computationally efficient techniques and do not require analytical expressions of the eingenstructure of the system. A well-balanced discretization of the bed-slope terms is developed in framework of the coupling approach. Finally, we demonstrate the robustness and accuracy of the proposed numerical scheme for the coupled system using several numerical tests.
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