溶质传输问题的一个经济差分格式

J4 ›› 2013, Vol. 48 ›› Issue (6): 75-79.

溶质传输问题的一个经济差分格式

张健青1,2,谢伟伟3,邹婉平3,温永艳3

1.中国矿业大学(北京)资源与安全工程学院, 北京 100083;
2.中石化胜利油田, 山东东营 257001; 3.山东大学数学学院, 山东济南 250100

收稿日期:2012-12-18 出版日期:2013-06-20 发布日期:2013-06-09
作者简介:张健青(1970- ),男,博士后,研究方向为能源安全经济投入研究. Email:zhangjianqing.slyt@sinopec.com
基金资助:
国家科技重大专项资助课题(2011ZX05011004,2011ZX05052); 山东省自然科学基金资助课题(ZR2011AM015)

An economical finite difference scheme for solute transport

ZHANG Jian-qing1,2, XIE Wei-wei3, ZOU Wan-ping3, WEN Yong-yan3

1. Faculty of Resources ＆ Safety Engineering, China University of Mining and Technology (Beijing),
Beijing 100083, China; 2. Shengli Oil Field, Dongying 257001, Shandong, China;
3. School of Mathematics, Shandong University, Jinan 250100, Shandong, China

Received:2012-12-18 Online:2013-06-20 Published:2013-06-09

摘要/Abstract

摘要：

将求解线性对流扩散方程的特怔线修正交替方向有限差分格式推广到含非线性扩散项和源汇项的溶质传输问题。对流项采用沿着特征线修正的差分结合插值技术进行离散,每个时间步顺序求解两个空间方向上的一维问题, 证明了格式的稳定性和收敛性。

关键词: 溶质传输;非线性扩散;非线性源汇项;交替方向;特征线修正技术

Abstract:

An economical finite difference method is proposed for solving the problem of solute transport with nonlinear diffusion and sourcesink terms. The transport term is discretized by the method of characteristics, and the difference systerm are docomposed to several problems of individual variable using alternating direction method. An interpolation operator is introduced for the technique of characteristics. The stability and convergence are analysed by energy method.

Key words: solute transport; nonlinear diffusion; nonlinear source／sink term; economical finite difference methods; charecteristics

张健青1,2,谢伟伟3,邹婉平3,温永艳3. 溶质传输问题的一个经济差分格式[J]. J4, 2013, 48(6): 75-79.

ZHANG Jian-qing1,2, XIE Wei-wei3, ZOU Wan-ping3, WEN Yong-yan3. An economical finite difference scheme for solute transport[J]. J4, 2013, 48(6): 75-79.

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