求解渗流方程的一种修正的中心型有限体积法  

A Modified Cell-Centered Finite Volume Method for Solving Filtration Equations

作　　者：陈国芳[1] 吴丹 吕俊良[2] CHEN Guofang;WU Dan;Lü Junliang(College of Minority Education,Jilin Provincial Institute of Education,Changchun 130022,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林省教育学院民族教育学院,长春130022 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2020年第5期1135-1141,共7页Journal of Jilin University:Science Edition

基　　金：挑战专题项目(批准号:TZ201602);吉林省科技发展计划项目(批准号:20200201259JC).

摘　　要：针对数值求解渗流方程时,使用标准有限体积法出现数值界面不能有效向前传播的“数值热障”现象,提出一种修正的有限体积法,该方法扩散系数的取值采用密度变量在两个相邻单元的代数平均值.数值实验结果表明,新格式可有效避免“数值热障”现象.When the filtration equation was solved numerically by the standard finite volume method,numerical solutions suffered from the“numerical hot barrier”phenomenon,in which numerical interface could not propagate forward correctly,we proposed a modified finite volume method.The diffusion coefficient of the method was the algebraic mean of the values of density variable at two neighbour elements.The results of numerical experiments show that the new scheme can effectively avoid“numerical hot barrier”phenomenon.

关 键 词：有限体积法 渗流方程 非线性迭代 Barenblatt解 

分 类 号：O241.82[理学—计算数学]