Using adaptive mesh methods is one of strategies to improve the numerical solutions of time dependent partial differential equations with singular or discontinuous solutions, such as shock waves, boundary layers and explosive waves. Shallow water equations are a nonlinear system of hyperbolic conservation laws. This system is problematic because it admits the discontinuous solutions and also, a discontinuous bathymetry can lead to the discontinuous solutions. In this paper, numerical solutions for shallow water equations with variable bathymetry are improved by using the moving mesh method with wave propagation algorithm. The results show that the moving mesh method leads to the highly accurate solutions around shocks and discontinuities in comparison with the fixed mesh.

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