A FULLY WELL-BALANCED, POSITIVE AND ENTROPY-SATISFYING GODUNOV-TYPE METHOD FOR THE SHALLOW-WATER EQUATIONS

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 a 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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Mathematics of Computation, American Mathematical Society, 2016, 85 (299), pp.1281-1307
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Christophe Berthon, Christophe Chalons. A FULLY WELL-BALANCED, POSITIVE AND ENTROPY-SATISFYING GODUNOV-TYPE METHOD FOR THE SHALLOW-WATER EQUATIONS. Mathematics of Computation, American Mathematical Society, 2016, 85 (299), pp.1281-1307. 〈hal-00956799v2〉

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