An efficient and flexible solver for the simulation of the morphodynamics of fast evolving flows on coarse sediment beaches

A well-balanced total variation diminishing-McCormack scheme is used to simulate the fast evolving flow on a mobile coarse sediments bed. The scheme is chosen because of its shock capturing capabilities and its relative simplicity, which allow different sediment transport formulae to be slotted in easily. A typical example of the kind of flows treated here is bore-driven wave run-up. The analogy with a dam-break on a mobile bed is used here to analyze the performance of the model. The model solves the nonlinear shallow water equations coupled with the Exner sediment balance equation for the mobile bed. Quasi-analytical solutions to this problem for different expressions for instantaneous sediment discharge formulae are used to test the performance of the scheme. Together with the existing solution for the Grass formula, a further solution is obtained for a different formula. Numerical tests were also carried out for a further formula that is an industry standard. The agreement of the results with the solutions is very good and consistent results were obtained for all the formulae tested. June 2011 10.1002/fld.2618 Research Article