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J4 ›› 2011, Vol. 46 ›› Issue (12): 6-12.

• 论文 • 上一篇    下一篇

多孔介质中可压缩混溶驱动问题的新型流线-扩散混合元方法

张建松1,牛海峰2   

  1. 1.中国石油大学(华东) 数学与计算科学学院, 山东 东营 257061;
    2.山东大学数学学院, 山东 济南 250100
  • 收稿日期:2010-09-25 出版日期:2011-12-20 发布日期:2011-12-24
  • 作者简介:张建松(1980- ),男,讲师,博士,研究方向为微分方程数值解. Email: jszhang@upc.edu.cn
  • 基金资助:

    山东省自然科学基金资助项目(ZR2010AL020);国家青年科学基金项目(11101431);中央高校基本科研业务费专项资金资助(12CX04082A,10CX04041A)

A new streamline-diffusion mixed finite element method for compressible  miscible displacement problem in porous medium

ZHANG Jian-song1, NIU Hai-feng2   

  1. 1. School of Mathematics and Computational Science, China University of Petroleum, Dongying 257061, Shandong, China;
    2. School of Mathematics, Shandong Universtiy, Jinan 250100, Shandong, China
  • Received:2010-09-25 Online:2011-12-20 Published:2011-12-24

摘要:

提出了一类新型流线-扩散混合有限元方法求解多孔介质中可压缩混溶驱动问题。引入分裂正定混合有限元方法求解抛物型的压力方程,混合有限元方程组是对称正定的,并且流函数方程不依赖于压力方程。采用标准的流线-扩散法求解对流扩散型的饱和度方程,分析了算法的收敛性并给出了相应的误差估计。

关键词: 流线扩散法;分裂正定混合元;混溶驱动;收敛性分析

Abstract:

A new streamline-diffusion mixed finite element procedure is constructed for solving compressible miscible displacement problem in porous medium. In this procedure, a splitting positive definite mixed element method, the parabolic-type pressure equation. Using a streamline-diffusion finite element method,  the convection-diffusion type concentration equation is solved. The coefficient matrix of the mixed system is symmetric and positive definite. The convergence of the procedure is studied and the corresponding error estimate is also given.

Key words: Streamline-diffusion; splitting positive definite mixed element; compressible miscible displacement; convergence analysis

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