Well-Balanced Finite Volume Scheme for Shallow Water Flooding and Drying Over Arbitrary Topography

Abstract

The depth-averaged shallow water equations based on Godunov-type fmite volume method are developed for unsteady flow over arbitrary topography with moving lateral boundaries caused by flooding or recession. An HILLC approximate Riemann solver is invoked to evaluate fluxes. A linear reconstruction procedure with WBAP-Ll limiter and modified 4 stages Runge-Kutta time stepping are employed to provide a second order accuracy that is free from spurious oscillations. Also, a robust technique is presented to efficiently and accurately simulate the movement of wet/dry fronts. The model predictions are compared with analytical solutions, experimental data and a two-dimensional dam-break event. Numerical results show that the model performs satisfactorily with respect to its effectiveness and robustness and thus has good application prospects.