一种新的混合有限体积元法求解一维多孔介质问题  

A New Mixed Finite Volume Element Method for Solving One-Dimensional Porous Medium Problems

作　　者：陈国芳[1] 黑圆圆 吕俊良[2] CHEN Guofang;HEI Yuanyuan;LV Junliang(School of Minority Education,Jilin Provincial Institute of Education,Changchun 130022,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]吉林省教育学院少数民族教育学院,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）》2019年第4期779-785,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11301214);国防基础科研核科学挑战专题项目(批准号:TZ2016002)

摘　　要：针对一维多孔介质问题用标准混合有限体积元法求解时会出现数值解波阵面不能向前传播的现象,提出一种新的混合有限体积元法求解退化问题,其中流变量仅包含原始变量对空间变量的导数.结果表明,该方法可避免数值解波阵面不能向前传播的现象,并能很好地捕捉数值解界面.数值实验验证了该方法的有效性。For the one-dimensional porous medium problem,wave front of the numerical solu tion could not propagate forward when the standard mixed finite volume element method was used to solve them,we proposed a new mixed finite volume element method for solving the degradation problem,in which the flux variable only included the derivative of the original variable to spacial variable. The results show that the method can avoid the phenomenon that wave front o f the numerical solution can not propagate forward,and can capture the interface of numerical solution well. The validity of the method is verified by numerical experiments.

关 键 词：多孔介质问题 混合有限体积元法 Picard迭代 

分 类 号：O241.82[理学—计算数学]