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A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows

Abstract : We consider the Saint-Venant system for shallow water flows with nonflat bottom. In past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady state reconstruction that allows one to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic steady states. It generalizes the now well-known hydrostatic solver, and like the latter it preserves the nonnegativity of the water height and satisfies a semidiscrete entropy inequality. An application to the Euler-Poisson system is proposed.
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François Bouchut, Tomás Morales de Luna. A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows. SIAM Journal on Numerical Analysis, Society for Industrial and Applied Mathematics, 2010, 48 (5), pp.1733-1758. ⟨10.1137/090758416⟩. ⟨hal-00693032⟩

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