扩散方程九点格式的保正性与极值性

doi:10.12288/szjs.s2020-0647

数值计算与计算机应用 ›› 2021, Vol. 42 ›› Issue (2): 134-145.DOI: 10.12288/szjs.s2020-0647

扩散方程九点格式的保正性与极值性

袁光伟

北京应用物理与计算数学研究所, 北京8009信箱, 北京 100094

收稿日期:2020-02-29 出版日期:2021-06-15 发布日期:2021-06-03
基金资助:
国家自然科学基金（批准号：11971069）与科学挑战专题（TZ2016002）资助.

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袁光伟. 扩散方程九点格式的保正性与极值性[J]. 数值计算与计算机应用, 2021, 42(2): 134-145.

Yuan Guangwei. POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS[J]. Journal on Numerica Methods and Computer Applications, 2021, 42(2): 134-145.

POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS

Yuan Guangwei

Institute of Applied Physics and Computational Mathematics, Beijing 100088, China

Received:2020-02-29 Online:2021-06-15 Published:2021-06-03

针对任意四边形网格上扩散方程已有的九点格式, 引入适当的限制器进行改写, 证明了所得到的非线性格式具有强保正性, 且该非线性格式的解若存在的话即为九点格式的一个正的解. 并进一步讨论了保持离散强极值原理的格式.

关键词： 扩散方程, 九点格式, 非线性格式, 强极值原理, 限制器

For the existing nine point scheme for diffusion equation on arbitrary quadrilateral meshes, a suitable limiter is introduced to modify discrete flux. It is proved that the obtained nonlinear scheme has strong positivity-preserving property, and the solution (if there exists one) of the nonlinear scheme is just a positive solution of the nine point scheme. Furthermore, the scheme of preserving discrete strong extremum principle is investigated.

Key words: Diffusion equation, nine point scheme, nonlinear scheme, strong extremum principle, limiter

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扩散方程九点格式的保正性与极值性

POSITIVITY AND EXTREMUM PRESERVING OF NINE POINT SCHEMES FOR DIFFUSION EQUATIONS

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