The main objective of this paper is to provide efficient and accurate sediment transport models and especially the bedload sediment tranport due to water evolution. The model is obtained by coupling the hydrodynamical component and the morphodynamical one. As our goal is to study coastal media, we chose the Shallow Water equations for the first component. For the other component the choice of the Exner law has been made using a function of the solid transport discharge, the Grass model. The coupled system of non linear partial differential equations is rewritten as a non-conservative hyperbolic system with source term that is solved by finite volume methods with flux limiters. Some numerical tests confirm the second-order of our numerical scheme.

This contribution deals with a high order Residual Distribution (RD) numerical scheme to simulate sediment transport. The morphodynamic model that has been used, couples shallow-water equations for the fluid flow and the Exner law for the sediment part. Thus, the choice of the approach by a non-conservative hyperbolic system has been made. Different schemes have already been applied to approximate the entropic solution for several test cases [10]. The one proposed in this paper resorts to RD-method, TVD Runge Kutta [27,31] and stabilisation upwind methods [13], with limiters. It can be viewed as an improvement of the generalized approximate Roe method [14,8,29] with some other good properties (Path-conservative, well-balanced...). Numerical results show the ability of the model in 1D to compute accurate solutions and to reproduce some classical test problems. The best results that we obtained, use MinMod flux limiters. This work is incorporated within the framework of the study of a sediment transport modelling. One aim of this contribution, is to provide first, an useful simulation tool, in the context of a 1D space-time problem. Considering the geophysical aspect,