Numerical simulation of the sediment transport models in shallow water flows based on new finite volume method

We propose a new finite volume method for the numerical solution of the sediment transport equations in one dimension. The model considered here consists of two components, namely a hydro-dynamical and a morphodynamical. The hydro-dynamical component is given by a shallow water system and the morphodynamical is described with a transport equation. To approximate the numerical solution of the considered models, we propose a two step finite volume scheme. The first step of the scheme depends on a diffusion control parameter which we modulate, using the limiters theory. This method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed finite volume method is well-balanced, non-oscillatory, conservative and suitable for the sediment transport equations which Riemann problems are difficult to solve. Numerical results are presented for the sediment transport equations. It is found that the proposed finite volume method offers a robust and accurate approach for solving the sediment transport equations.