A simple well-balanced and positive numerical scheme for the shallow-water system

Abstract : This work considers the numerical approximation of the shallow-water equations. In this context, one faces three important issues related to the well-balanced, positivity and entropy-preserving properties, as well as the ability to consider vacuum states. We propose a Godunov-type method based on the design of a three-wave Approximate Riemann Solver (ARS) which satisfies the first two properties and a weak form of the last one together. Regarding the entropy, the solver satisfies a discrete non-conservative entropy inequality. From a numerical point of view, we also investigate the validity of a conservative entropy inequality.
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Communications in Mathematical Sciences, International Press, 2015, 13 (5), pp.1317-1332. 〈10.4310/CMS.2015.v13.n5.a11〉
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Emmanuel Audusse, Christophe Chalons, Philippe Ung. A simple well-balanced and positive numerical scheme for the shallow-water system. Communications in Mathematical Sciences, International Press, 2015, 13 (5), pp.1317-1332. 〈10.4310/CMS.2015.v13.n5.a11〉. 〈hal-01083364v2〉

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