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A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids. (English) Zbl 1390.76516

Summary: We introduce a new second-order central-upwind scheme for shallow water equations on the unstructured quadrilateral grids. We propose a new technique for bottom topography approximation over quadrilateral cells as well as an efficient water surface correction procedure which guarantee the positivity of the computed fluid depth. We also design a new quadrature for the discretization of the source term, using which the new scheme exactly preserves “lake at rest” steady states. We demonstrate these features of the new scheme as well as its high resolution and robustness and its potential advantages over the triangular central-upwind scheme in a number of numerical examples.

MSC:

76M12 Finite volume methods applied to problems in fluid mechanics
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
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