The Neumann boundary condition for the two-dimensional Lax–Wendroff scheme

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-11-15 DOI:10.4310/cms.2023.v21.n8.a1

Antoine Benoit, Jean-François Coulombel

引用次数: 0

Abstract

We study the stability of the two-dimensional Lax–Wendroff scheme with a stabilizer that approximates solutions to the transport equation. The problem is first analyzed in the whole space in order to show that the so-called energy method yields an optimal stability criterion for this finite difference scheme. We then deal with the case of a half-space when the transport operator is outgoing. At the numerical level, we enforce the Neumann extrapolation boundary condition and show that the corresponding scheme is stable. Eventually we analyze the case of a quarter-space when the transport operator is outgoing with respect to both sides. We then enforce the Neumann extrapolation boundary condition on each side of the boundary and propose an extrapolation boundary condition at the numerical corner in order to maintain stability for the whole numerical scheme.

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二维Lax-Wendroff格式的Neumann边界条件

我们研究了二维Lax-Wendroff格式的稳定性，该格式具有近似输运方程解的稳定剂。首先在整个空间中对问题进行分析，以证明所谓的能量法对这种有限差分格式给出了最优稳定性判据。然后，我们处理半空间的情况，当传输算子是外向的。在数值层面上，我们执行了Neumann外推边界条件，并证明了相应格式是稳定的。最后，我们分析了四分之一空间中运输算子相对于两边都是外向的情况。然后，我们在边界的每一侧强制执行诺伊曼外推边界条件，并在数值角处提出外推边界条件，以保持整个数值方案的稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.