The improved surface gradient method for flows simulation in variable bed topography channel using TVD-MacCormack scheme

This paper reports four different approaches to discretize the source terms for the simulation of one-dimensional open-channel flows with rapidly varied bottom topography using TVD-MacCormack scheme. Compared with other high-resolution shock-capturing schemes, MacCormack-type predictor-corrector method is easy to implement and does not present any additional difficulty in dealing with the source terms. To avoid the generation of artificial numerical waves, if the bottom topography shows strong variation, special treatment of the source terms is still required to eliminate or reduce the artificial numerical error caused by adding TVD corrections to the method. The computed results demonstrated that the improved surface gradient method is more suitable for simulating open-channel flow with highly irregular bed topography by using the surface gradient instead of the depth gradient for TVD corrections and considering the balancing of the source terms and the flux gradients.