Mathematical model and numerical method for spontaneous potential log in heterogeneous formations  

作　　者：潘克家 谭永基 胡宏伶 

机构地区：[1]School of Mathematical Sciences, Fudan University [2]College of Mathematics and Computer Science, Hunan Normal University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第2期209-219,共11页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 10431030);the Shanghai Natural Science Foundation (No. 08ZR1401100)

摘　　要：This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.This paper introduces a new spontaneous potential log model for the case in which formation resistivity is not piecewise constant. The spontaneous potential satisfies an elliptic boundary value problem with jump conditions on the interfaces. It has beer/ shown that the elliptic interface problem has a unique weak solution. Furthermore, a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic problems. Numerical results show validity and effectiveness of the proposed method.

关 键 词：spontaneous potential log elliptic interface problems mathematical model numerical simulation 

分 类 号：O241.8[理学—计算数学]