• 论文 • 上一篇    

扩散方程九点格式的保正性与极值性

袁光伟   

  1. 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 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.

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   

  1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2020-02-29 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.
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.

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