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| 油水驱动半正定问题迎风混合元格式及其数值分析 | |
| 引用本文： | 宋怀玲. 油水驱动半正定问题迎风混合元格式及其数值分析[J]. 应用数学, 2005, 18(4): 610-618 |
| 作者姓名： | 宋怀玲 |
| 作者单位： | 湖南大学数学与计量经济学院,湖南,长沙,410082 |
| 基金项目： | Foundation item：Supported by the Major State Basic Research of China （1999032803）, the National Natural 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. |
| 关 键 词： | 半正定 不可压 迎风 混合元 |
| 文章编号： | 1001-9847(2005)04-0610-09 |
| 收稿时间： | 2004-10-25 |
| 修稿时间： | 2004-10-25 |
Upwinding-mixed Methods for Positive Semi-definite Problem of Two Phase Miscible Flow in Porous Media |
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| SONG Huai-ling. Upwinding-mixed Methods for Positive Semi-definite Problem of Two Phase Miscible Flow in Porous Media[J]. Mathematica Applicata, 2005, 18(4): 610-618 | |
| Authors: | SONG Huai-ling |
| Affiliation: | College of Mathematics and Econometrics, Hunan University , Changsha 410082 ,China |
| Abstract: | The miscible displacement of one incompressinble 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 matrix 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. |
| Keywords: | Positive semi-definite Incompressible Upwinding Mixed finite elements. |
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