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

作　　者：袁光伟[1] Yuan Guangwei(Institute of Applied Physics and Computational Mathematics,Beijing 100088,China)

机构地区：[1]北京应用物理与计算数学研究所,北京100094

出　　处：《数值计算与计算机应用》2021年第2期134-145,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(批准号:11971069);科学挑战专题(TZ2016002)资助。

摘　　要：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.

关 键 词：扩散方程 九点格式 非线性格式 强极值原理 限制器 

分 类 号：O175[理学—数学]