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An unstructured finite volume algorithm for nonlinear two-dimensional shallow water equation. (English) Zbl 1207.76097
Summary: An unstructured finite volume numerical algorithm was presented for solution of the two-dimensional shallow water equations, based on triangular or arbitrary quadri-lateral meshes. The Roe type approximate Riemann solver was used to the system. A second-order TVD scheme with the van Leer limiter was used in the space discretization and a two-step Runge-Kutta approach was used in the time discretization. An upwind, as opposed to a pointwise, treatment of the slope source terms was adopted and the semi-implicit treatment was used for the friction source terms. Verification for two-dimension dam-break problems are carried out by comparing the present results with others and very good agreement is shown.

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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