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

被引：47

作者：

Berthon, Christophe ^{[1
]}

Chalons, Christophe

机构：

[1] Univ Nantes, CNRS UMR 6629, Lab Math Jean Leray, 2 Rue Houssiniere,BP 92208, F-44322 Nantes, France

来源：

MATHEMATICS OF COMPUTATION | 2016年 / 85卷 / 299期

关键词：

Shallow-water equations; steady states; finite volume schemes; well-balanced property; positive preserving scheme; entropy preserving scheme; DISCONTINUOUS GALERKIN METHODS; VOLUME WENO SCHEMES; HYPERBOLIC SYSTEMS; HYDROSTATIC RECONSTRUCTION; CONSERVATION-LAWS; ORDER; RELAXATION; DYNAMICS; SOLVER;

D O I：

10.1090/mcom3045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：1281 / 1307

页数：27

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