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.
https://hal-upec-upem.archives-ouvertes.fr/hal-00693032
Contributor : Admin Lama <>
Submitted on : Tuesday, May 1, 2012 - 7:38:55 PM Last modification on : Monday, March 30, 2020 - 12:04:02 PM
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⟩