Abstract: TVD Lax-Wendroff schemes for the computation of weak solution of hyperbolic conservation law are extended to the gencral shallow-water equations with thc arbitrary variation of the section shape with distance. A second-order accurate finite difference scheme ispresented. The new scheme can be applied to simulating the dam-break flood wave propagation in the natural river courses. Numerical examples are provided to test the performance of the method. Numerical experirnents with dam-break problems in the practical natural cascade reservoirs show that the scheme is stable and robust.

Key words: Shallow water equations, Finite difference method, Natural river courses, Dambreak waves, TVD