A large time step Godunov scheme for free-surface shallow water equations

An algorithm for simulating free surface flows is presented using large time step based on the wave-propagation method proposed by LeVeque, and an exact Riemann solver is used. A multiple wave approximation approach was suggested for eliminating the discontinuities found in the rarefaction fans of dam-breaking flows. In addition, we use the random choice method to reduce non-physical oscillations. Applications demonstrate that the algorithm proposed in this paper can considerably increase the CFL number up to 25 when modeling dam-break flows, while retaining satisfactory accuracy and efficiency. This suggests that our algorithm has the potential to be applied to modeling free surface flows.