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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. [ABSTRACT FROM AUTHOR]

Abstract: A simple solver is proposed for the numerical solution of density-driven multi-layer shallow water flows. The governing equations consist on coupling the multi-layer shallow water equations for the hydraulic variables with suspended sediment transport equations for the concentration variables. The layers can be formed in the shallow water model based on the variation of water density which may depend on the water temperature and salinity. At each time step, the method consists of two stages to update the numerical solution. In the first stage, the multi-layer shallow water equations are rewritten in a non-conservative form and the intermediate solutions are calculated using the modified method of characteristics. In the second stage, the numerical fluxes are reconstructed from the intermediate solutions in the first stage and used in the conservative form of the multi-layer shallow water equations. The proposed method avoids Riemann problem solvers and it is suitable for multi-layer shallow water equations on non-flat topography. Several numerical results are presented to illustrate the performance of the proposed finite volume method. The computed results confirm its capability to solve multi-layer shallow water equations for density-driven flows over flat and non-flat bottom topography. [Copyright &y& Elsevier]

Abstract: We propose a new numerical method for solving the equations of coupled sediment transport and bed morphology by free-surface water flows. The mathematical formulation of these models consists of the shallow water equations for the hydraulics, an advection equation for the transport of sediment species, and an Exner equation for the bedload transport. The coupled problem forms a one-dimensional hyperbolic system of conservation laws with geometric source terms. The proposed numerical method combines the method of characteristics with a finite volume discretization of the system. The combined method is simple to implement and accurately resolves the governing equations without relying on Riemann problem solvers. Numerical results are presented for several test examples on sediment transport and bed morphology by free-surface water flows. [Copyright &y& Elsevier]