油水驱动半正定问题迎风混合元格式及其数值分析(英文)  

Upwinding-mixed Methods for Positive Semi-definite Problem of Two Phase Miscible Flow in Porous Media

作　　者：宋怀玲[1] 

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082

出　　处：《应用数学》2005年第4期610-618,共9页Mathematica Applicata

基　　金：Supported by the Major State Basic Research of China (1999032803) ,the NationalNatural Science Foundation of China (10271066 ,10372052) ,and the Doctorate Foundation of the Minis-try of Education of China (20030422047)

摘　　要：研究了不可压缩油水两相渗透流驱动问题.在扩散矩阵仅是半正定的假设条件下,提出了迎风混合元方法.混合元方法近似压力方程,饱和度方程的对流项用Godunov迎风格式来处理,扩散项则用推广的混合元来逼进,并推导出格式的误差估计.此种格式的优越性表现在两个方面:首先是饱和度方程的扩散矩阵仅是半正定的;二是摒弃了特征格式所限制的周期性条件,更适用于实际问题.The miscible displacement of one ineompressinble fluid by another in a porous medium is governed by a system of two equations,one of elliptic form for the pressure and the other of parabolic form for the concentration of one of the fluids. We presented the upwind-mixed method for the case D（u）≥0. The pressure is approximated by a mixed finite element method and the concentration by a method which upwinds the convection and incorporates diffusion using an expanded mixed finite element method. The scheme improves upon previously methods in two respects：first,the diffusion ma rix is only positive semidefinite, and second,the scheme is not to be needed the Ω-periodic condition for the method of characteristics. Error estimates are derived when the imposed external flows are smoothly distributed. A numerical experiment is given.

关 键 词：半正定 不可压 迎风 混合元 

分 类 号：O241[理学—计算数学]