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Finite volume scheme for numerical simulation of the sediment transport model. (English) Zbl 1428.76123

Summary: In this paper, we propose and apply a modified Rusanov scheme for numerical solution of the sediment transport model in one and two dimensions. This model consists of two parts, the first part is modeled by shallow water equations and the second part is described by the bed-load transport equation. The scheme consists of a predictor stage scheme including a local parameter of control. It is responsible for the numerical diffusion. To control this parameter, we use a strategy depending on limiter theory. In the corrector stage, we used special treatment of the bed to get a well-balanced discretization between the flux gradient and source term. Some numerical results are presented for the sediment transport equation in two forms called \(A\)-formulation and \(C\)-formulation. These results show that the finite volume scheme is accurate and robust for solving the sediment transport equation in one and two dimensions.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
86A05 Hydrology, hydrography, oceanography
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