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The composite finite volume method on unstructured meshes for the two-dimensional shallow water equations. (English) Zbl 1055.76532
Summary: 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 on 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 followcd by a diffusive Lax-Friedrich-type step, which filters out the oscillations around shocks typical for LaxWendroff 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 highly stable.

MSC:
76M12 Finite volume methods applied to problems in fluid mechanics
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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