High resolution reconstruction techniques for sediment transport in shallow water flows

Abstract

In this study, a numerical approximation is proposed for bed load sediment transport for rapidly varying flows. Hydrodynamics and morphodynamics of the flow are modeled by the two-dimensional Saint Venant and sediment continuity equations, respectively. The equations are coupled and the solution is evolved in one time step by the Godunov type finite volume method. For temporal discretization a third-order TVD Runge-Kutta method is used. For a spatial accuracy, a gradient reconstruction is performed by two high resolution methods; A third order Weighted Essentially Non oscillatory (WENO) scheme, and another gradient reconstruction together with a limiting technique. Both techniques are employed on unstructured triangular meshes, which are advantageous over structured meshes when local grid refinement is desired in vicinity of abrupt geometry modulations. These methods reconstruct cell centered variables at interface of control volume for accurate approximation of flow information. Fluxes at the interfaces are computed by approximate Riemann solvers. The applicability of the proposed model for a hyperbolic system is studied by simulating several test cases and effects of both the reconstruction methods on the results are investigated.