Two-dimensional sediment transport models in shallow water equations. A second order finite volume approach on unstructured meshes

In this paper, we study the numerical approximation of bedload sediment transport due to shallow layer flows. The hydrodynamical component is modeled by a 2D shallow water system and the morphodynamical component by a solid transport discharge formula that depends on the hydrodynamical variables. The coupled system can be written as a nonconservative hyperbolic system. To discretize it, first we consider a Roe-type first order scheme as well as a variant based on the use of flux limiters. These first order schemes are then extended to second order accuracy by means of a new MUSCL-type reconstruction operator on unstructured meshes. Finally, some numerical tests are presented.