两相多组分流有限元方法的收敛性

J4 ›› 2012, Vol. 47 ›› Issue (2): 19-25.

两相多组分流有限元方法的收敛性

于金彪^1,2,席开华^3*,戴涛^2,鲁统超³,杨耀忠²,任永强³,程爱杰³

1.中国石油大学(北京)地球科学学院, 北京 102249;
2.中国石化股份胜利油田分公司地质科学研究院, 山东东营 257015; 3.山东大学数学学院, 山东济南 250100

收稿日期:2011-05-01 出版日期:2012-02-20 发布日期:2012-12-24
通讯作者: 席开华(1986- ),男,科研助理，研究方向为油藏数值模拟. Email: ckh009-009@163.com
作者简介:于金彪(1970- ),男,博士研究生,研究方向为油田开发与油藏数值模拟. Email: yjb0920@126.com
基金资助:
国家科技重大专项资助课题(2008ZX05011004)

Convergence of the finite element method for two-phase multi-component flow in porous media

YU Jin-biao^1,2, XI Kai-hua^3*, DAI Tao², LU Tong-chao³, YANG Yao-zhong²,

1. College of Geosciences, China University of Petroleum, Beijing 102249, China;
2. Research Institute of Geological Science, Shengli Oilfield Company Ltd., Dongying 257015, Shandong, China;
3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2011-05-01 Online:2012-02-20 Published:2012-12-24

摘要/Abstract

摘要：

考虑多孔介质中两相多组分不可压缩不混溶驱动问题,给出了描述该问题的数学模型, 包含椭圆型压力方程,对流扩散型饱和度方程和组分浓度方程,采用标准Galerkin有限元方法, 给出了隐式全离散格式,并利用能量法得到了最优H¹模先验误差估计,时间收敛阶为一阶。

关键词: 多组分不混溶流动;Galerkin有限元;全离散格式;误差估计

Abstract:

The mathematical model for describing two phase incompressible immiscible displacement flow with multi-components in porous media is considered. A global formulation of the governing equations, including pressure, saturation and concentration equations is constructed. For the system, a full-discrete scheme is formulated by the standard Galerkin finite element method and the optimal error estimate in H1 norm is derived.

Key words: multi-components immiscible displacement; Galerkin method; full-discrecte scheme; error estimates

于金彪1,2,席开华3*,戴涛2,鲁统超3,杨耀忠2,任永强3,程爱杰3. 两相多组分流有限元方法的收敛性[J]. J4, 2012, 47(2): 19-25.

YU Jin-biao1,2, XI Kai-hua3*, DAI Tao2, LU Tong-chao3, YANG Yao-zhong2, . Convergence of the finite element method for two-phase multi-component flow in porous media[J]. J4, 2012, 47(2): 19-25.

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