三维非线性对流扩散问题的数值方法在渗流力学的应用

袁益让; 杜宁; 王文洽; 程爱杰; 韩玉笈

三维非线性对流扩散问题的数值方法在渗流力学的应用

1.
山东大学数学研究所,济南 250100;2.胜利石油管理局物探研究院胜利石油管理局物探研究院,山东东营 257022

基金项目: 国家自然科学基金资助项目(10370252;10271066);国家重点基础研究专项经费资助项目(G19990328);国家攻关基金资助项目(20050200069);国家教育部博士点基金资助项目(20030422047)

详细信息

作者简介:
袁益让(1935- ),男,教授(联系人.Tel:+86-531-88364732;Fax:+86-531-88564652;E-mail:yryuan@sdu.edu.cn).

中图分类号: O241.82
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出版历程
- 收稿日期: 2004-10-18
- 修回日期: 2006-01-18
- 刊出日期: 2006-05-15

Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media

1.
Institute of Mathematics, Shandong University, Jinan 250100, P. R. China;

摘要

摘要: 对三维非线性对流扩散问题提出一类适合并行计算的二阶迎风分数步差分格式，采用分数步技术，将三维问题化为连续解3个一维问题计算．利用变分形式、能量方法、差分算子乘积交换性、高阶差分算子的分解、微分方程先验估计的理论和技巧，得到收敛性的最佳阶的误差估计．该方法已成功的应用油资源运移聚集渗流力学数值模拟计算、海水入侵预测和防治的工程实践中．
- 非线性对流扩散 /
- 渗流力学 /
- 迎风分数步 /
- 差分方法 /
- 收敛性 /
- 油资源数值模拟
Abstract: For the three-dimensional convection-dominated problem of dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic were put forward. Fractional steps techniques were needed to convert a multi-dimensional problem into a series of successive one-dimensional problems. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators, and the theory of prior estimates were adopted. Optimal order estimates are derived to determine the error in the second order approximate solution. These methods have already been applied to the numerical simulation of migration-accumulation of oil resources and predicting the consequences of seawater intrusion and protection projects.
- nonlinear convection-dominated /
- dynamics of fluids /
- upwind fractional steps /
- finite difference method /
- convergence /
- numerical simulation

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参考文献(18)

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三维非线性对流扩散问题的数值方法在渗流力学的应用

作者简介:
袁益让(1935- ),男,教授(联系人.Tel:+86-531-88364732;Fax:+86-531-88564652;E-mail:yryuan@sdu.edu.cn).

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Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media

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三维非线性对流扩散问题的数值方法在渗流力学的应用

作者简介: 袁益让(1935- ),男,教授(联系人.Tel:+86-531-88364732;Fax:+86-531-88564652;E-mail:yryuan@sdu.edu.cn).

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出版历程

Numerical Method for the Three-Dimensional Nonlinear Convection-Dominated Problem of Dynamics of Fluids in Porous Media

计量

出版历程

目录

作者简介:
袁益让(1935- ),男,教授(联系人.Tel:+86-531-88364732;Fax:+86-531-88564652;E-mail:yryuan@sdu.edu.cn).