A Coupled Sediment Transport Model for Flow over Movable Bed

Abstract

A numerical approximation for bed load sediment transport due to shallow-water flows is studied. Flows over an erodible bed are solved by assuming that the dynamics of the bed load problem is described by two mathematical models: the hydrodynamic model, represented by the depth integrated shallow-water equations, and the morphological model: Exner equation. The model solves the coupled shallow-water and Exner equations, with the interface fluxes evaluated by a Harten-Lax van Leer-Contact (HLLC) approximate Riemann solver for hydrodynamic part and HLL scheme for morphological part. The domain is discretized by triangular grid system which facilitates representing complex domains. A special treatment of the source terms by surface gradient method makes the scheme stable and physically balanced. The model employs Godunov- type finite volume algorithm, with second-order accuracy in space and time. Spatial second-order accuracy is guaranteed by employing multidimensional gradient reconstruction method; and predictor-corrector scheme is used to ensure a second-order accurate solution in time. Finally, some numerical tests are presented to verify the applicability and accuracy of the proposed numerical model.