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A HIGH RESOLUTION FINITE VOLUME METHOD FOR SOLVING SHALLOW WATER EQUATIONS
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ABSTRACT: A high-resolution finite volume numerical method for solving the shallow water equations is developed in this paper. In order to extend finite difference TVD scheme to finite volume method, a new geometry and topology of control bodies is defined considering the corresponding the relationships between nodes and elements. This solver is implemented on arbitrary quadrilateral meshes and their satellite elements, and based on a second-order hybrid type TVD scheme in space discretization and a two-step Runge-Kutta method in time discretization. Then it is used to deal with two typical dam-break problems and very satisfactory results are obtained comparing with other numerical solutions. It can be considered as an efficient implement for the computation of shallow water problems, especially concerning those having discontinuities, subcritical and supercritical flows and with complex geometries.
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