The composite finite volume method on unstructured meshes for the two-dimensional shallow water equations

A composite finite volume method (FVM) is developed on unstructured triangular meshes and tested for the two-dimensional free-surface flow equations. The methodology is based on the theory of the remainder effect of finite difference schemes and the property that the numerical dissipation and dispersion of the schemes are compensated by each other in a composite scheme. The composite FVM is formed by global composition of several Lax-Wendroff-type steps followed by a diffusive Lax-Friedrich-type step, which filters out the oscillations around shocks typical for the Lax-Wendroff scheme. To test the efficiency and reliability of the present method, five typical problems of discontinuous solutions of two-dimensional shallow water are solved. The numerical results show that the proposed method, which needs no use of a limiter function, is easy to implement, is accurate, robust and is highly stable. Copyright (C) 2001 John Wiley & Sons, Ltd.