High-resolution Fully Coupled Shallow Water Flow and Sediment Transport Model on Unstructured Grids

Sediment transport governs the erosion and deposition processes, which impacts the topography of the earth, the movement of sediment with fluid is among the most complex and least understood processes in nature. Current process-based sediment transport models use partial differential equations that are referred to as conservation laws to describe flow and transport processes. This work extends the idea of the multi-mode sediment transport model to present a two-dimensional, non-equilibrium, total load sediment transport model. A depth-averaged shallow water flow and sediment transport model is used for describing the mass and momentum exchange of sediment-water mixture flow, which is numerically solved by a second-order Godunov-type scheme. A novel Total Variation Diminishing Monotonic Upwind Scheme for Conservation Law (TVD-MUSCL) scheme is applied here for extending the original scheme to a second-order on unstructured grids. Sediment is transported as depth-averaged volume concentration of the mixture flow and a sediment velocity ratio is introduced account for the velocity difference for the sediment and fluid. A modified Harten, Lax and van Leer Riemann solver with the contact wave restored (HLLC) is derived for the flux calculation based on a new wave pattern involving the sediment velocity ratio. The hydrostatic reconstruction is added for the wet and dry interface and the gravity source terms are considered as slope fluxes which include the density change caused by the concentration difference from the cell centre to the edge centre. The other related source term calculation is enhanced by means of a novel splitting-point implicit discretization. The topography slope effect is introduced by modifying the critical shear stress, with two treatments being discussed. The numerical scheme is tested in several examples (dam-break, dyke over-topping) that comprise both fixed and movable beds against experimental data and three-dimensional data from the literature. The model predictions show good agreement with measurements and demonstrate the new capabilities, however, there is some reservation for cases where local three-dimensional effects dominate.