Numerical Modelling of Erosion and Deposition with Cohesive and Non-Cohesive Sediments

In this work, a robust two-dimensional model is constructed to simulate river erosion and deposition of cohesive and non-cohesive sediment. The numerical model is constructed based on the shallow water equations with sediment-flow interactions that incorporates a sediment transport model including, significantly, the evolution of the bed profile. The governing equations are solved explicitly using finite volume method using a Godunov type approximate Riemann solver. A spatially first order accurate and numerically robust Harten-Lax-van Leer (HLL) solver is utilised to calculate the fluxes at cell faces. A Courant-Friedrichs-Lewy (CFL) type criterion governs temporal stability of the solver.
The sediment transport component of the model consists of two different elements: the first, HMD-NC, is constructed to simulate flow over a movable bed with non-cohesive materials; and the second, HMD-C, is constructed to simulate the flow over a movable bed of cohesive materials. The models are tested and validated against experimental and theoretical works from published literature. The results show good agreement with the measurements, demonstrating that the models are both capable of predicting the spatial and temporal changes of the flow and bed change effectively. In a case study is used to demonstrate the cohesive model, HMD-C, which shows the impact of employing different formulations for erosion rates of the channel bed in which significant differences are seen in resulting solutions. An intensive investigation of the model parameters on the numerical result is presented. It is found that the model is particularly sensitive to certain parameters such as erodibility, Manning’s roughness, and the critical shear stress for erosion. While others such as critical shear stress for deposition, bed porosity, and the settling velocity show very low influence on the erosion.