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

Berthon, Christophe; Chalons, Christophe

doi:10.1090/mcom3045

A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations
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by Christophe Berthon and Christophe Chalons;

Math. Comp. 85 (2016), 1281-1307

DOI: https://doi.org/10.1090/mcom3045

Published electronically: September 15, 2015

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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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