Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods

This paper is concerned with the numerical approximation of bedload sediment transport due to water evolution. For the hydrodynamical component we consider Shallow Water equations. The morphodynamical component is defined by a continuity equation, which is defined in function of the solid transport discharge. We present several deterministic models, such as Meyer-Peter & Müller, Van Rijn or Grass model. We also present an unified definition for the solid transport discharge, and we compare with Grass model. Both components define a coupled system of equations that can be rewrite as a non-conservative hyperbolic system. To discretize it, we consider finite volume methods with or without flux limiters and high order state reconstructions. Finally we present several tests, where we observe numerically the order of the numerical schemes. Comparisons with analytical solutions and experimental data are also presented.