An Energy-Stable High-Order Central Difference Scheme for the Two-Dimensional Shallow Water Equations

被引：0

作者：

Matthew Brown

Margot Gerritsen

机构：

[1] University of Auckland,Department of Engineering Science, School of Engineering

[2] Stanford University,Department of Petroleum Engineering, Green Earth Sciences Building

来源：

Journal of Scientific Computing | 2006年 / 28卷

关键词：

Shallow water equations; entropy-splitting; semi-discrete energy estimate; central finite difference scheme;

D O I：

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学科分类号：

摘要：

An energy-stable high-order central finite difference scheme is derived for the two-dimensional shallow water equations. The scheme is mathematically formulated using the semi-discrete energy method for initial boundary value problems described in Olsson (1995, Math. Comput. 64, 1035–1065): after symmetrizing the equations via a change to entropy variables, the flux derivatives are entropy-split enabling the formulation of a semi-discrete energy estimate. We show experimentally that the entropy-splitting improves the stability properties of the fully discretized equations. Thus, the dependence on numerical dissipation to keep the scheme stable for long term time integrations is reduced relative to the original unsplit form, thereby decreasing non-physical damping of solutions. The numerical dissipation term used with the entropy-split equations is in a form which preserves the semi-discrete energy estimate. A random one-dimensional dam break calculation is performed showing that the shock speed is computed correctly for this particular case, however it is an open question whether the correct shock speed will be computed in general

引用

页码：1 / 30

页数：29

共 29 条

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