A numerical scheme for morphological bed level calculations

The typical equation for bed level change in sediment transport in river, estuary and near shore systems is based on conservation of sediment mass. It is generally a nonlinear conservation equation for bed level. The physics here are similar to shallow water wave equations and gas dynamics equation which will develop shock waves in many circumstances. Many state-of-art morphological models use classical lower order Lax–Wendroff or modified Lax–Wendroff schemes for morphology which are not very stable for long time sediment transport processes simulation. Filtering or artificial diffusion are often added to achieve stability. In this paper, several shock capturing schemes are discussed for simulating bed level change with different accuracy and stability behaviors. The conclusion is in favor of a fifth order Euler-WENO scheme which is introduced to sediment transport simulations here over other schemes. The Euler-WENO scheme is shown to have significant advantages over schemes with artificial viscosity and filtering processes, hence is highly recommended especially for phase-resolving sediment transport models.