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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.

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