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Moving-water equilibria preserving HLL-type schemes for the shallow water equations. (English) Zbl 1463.76035

Summary: We construct new Harten-Lax-van Leer (HLL)-type moving-water equilibria preserving upwind schemes for the one-dimensional Saint-Venant system of shallow water equations with nonflat bottom topography. The designed first- and second-order schemes are tested on a number of numerical examples, in which we verify the well-balanced property as well as the ability of the proposed schemes to accurately capture small perturbations of moving-water steady states.

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
86A05 Hydrology, hydrography, oceanography
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