Abstract: A Second-order accurate TVD scheme for shallow water equations is presented. A simple TVD Runge-Kutta type time discretization and a symmetric space discretization based on the slope limiter is used. The mumerical dissipation term is constructed based on the local prism river flows. The main advantage of the scheme stems from the ability to compute the weak solutions of unsteady free-surface flows in the natural river courses and the simplicity. Constant still water solution in the natural river courses of the uneven bottom channel can be exactly compted. Verification of the scheme for the dam-break problem in the channel is made by comparison with analytical solution and good agreement is found. Numerical experiments with the dam-break problem in the practical natural cascade reservoirs show the scheme is stable and robust.

Key words: shallow water equations, natural river courses, finite difference method, RungeKutta method, TVD