Abstract: Exact Riemann solver and wave propagation method are combined to achieve large time-step scheme (LTS) in shallow water flow. Multi-wave approximation is adapted to solve discontinuity of rarefaction, and a random choice method (RCM) is used to eliminate oscillation in nonlinear hyperbolic systems. Efficiency is increased in LTS scheme with multi-wave approximation and random choice method as large Courant-Fridrichs-Lewy (CFL) number is imposed.

Key words: random choice method (RCM), multi-wave approximation, large-time step (LTS) scheme, shallow water equations