论带稳定修正的中央差分方案在三维传输方程中的稳定性

IF 0.7 4区数学 Q3 MATHEMATICS, APPLIED

Computational Mathematics and Mathematical Physics Pub Date : 2024-06-13 DOI:10.1134/s0965542524700271

V. P. Zhukov

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引用次数: 0

摘要

摘要一般认为，在三维情况下，对输运方程进行稳定修正的中心差分方案是有条件稳定的。本文指出，严格来说，该方案是绝对不稳定的。然而，随着库朗参数趋于零，波矢量空间中的不稳定谐波区域及其增量很快趋于零，这使得成功使用该方案成为可能。因此，更正确的说法是这种方案实际上的条件稳定性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation

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On the Stability of a Central Difference Scheme with a Stabilizing Correction for the 3D Transport Equation

Abstract

It is generally accepted that the central differences scheme with a stabilizing correction for the transport equation in the 3D case is conditionally stable. This article shows that, strictly speaking, this scheme is absolutely unstable. However, the region of unstable harmonics in the wave vector space and their increments quickly tend to zero as the Courant parameter tends to zero, which makes it possible to successfully use this scheme. Therefore, it is more correct to talk about the practically conditional stability of this scheme.

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来源期刊

Computational Mathematics and Mathematical Physics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.50

自引率

14.30%

发文量

125

审稿时长

4-8 weeks

期刊介绍： Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.