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A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations


Authors: Christophe Berthon and Christophe Chalons
Journal: Math. Comp. 85 (2016), 1281-1307
MSC (2010): Primary 65M60, 65M12, 76M12, 35L65
DOI: https://doi.org/10.1090/mcom3045
Published electronically: September 15, 2015
MathSciNet review: 3454365
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Abstract: This work is devoted to the derivation of a fully well-balanced numerical scheme for the well-known shallow-water model. During the last two decades, several well-balanced strategies have been introduced with special attention to the exact capture of the stationary states associated with the so-called lake at rest. By fully well-balanced, we mean here that the proposed Godunov-type method is also able to preserve stationary states with non zero velocity. The numerical procedure is shown to preserve the positiveness of the water height and satisfies a discrete entropy inequality.


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Additional Information

Christophe Berthon
Affiliation: Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France

Christophe Chalons
Affiliation: Laboratoire de Mathématiques de Versailles, UMR 8100, Université de Versailles Saint-Quentin-en-Yvelines, UFR des Sciences, bâtiment Fermat, 45 avenue des Etats-Unis, 78035 Versailles cedex, France

DOI: https://doi.org/10.1090/mcom3045
Keywords: Shallow-water equations, steady states, finite volume schemes, well-balanced property, positive preserving scheme, entropy preserving scheme
Received by editor(s): May 15, 2014
Received by editor(s) in revised form: December 3, 2014
Published electronically: September 15, 2015
Article copyright: © Copyright 2015 American Mathematical Society