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A flux-splitting solver for shallow water equations with source terms. (English) Zbl 1033.76033

Summary: This paper introduces a stable flux-splitting solver for one-dimensional shallow water equations. This solver is specifically designed to satisfy a strengthened consistency condition for stationary solutions that ensures the stability and accuracy of the scheme. It applies to channels with variable depth and width, including terms modelling friction at bottom and vertical walls. Some numerical tests by comparison to both analytical solutions and experimental measurements show the good performances of the scheme.

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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