非线性渗流耦合系统的数值方法及其应用  

Numerical Method for the Nonlinear Two-Phase Displacement Problem and Its Application

作　　者：袁益让[1] 梁栋[1] 芮洪兴[1] 杜宁[1] 王文洽[1] 李家春(推荐) 

机构地区：[1]山东大学数学研究所,济南250100 [2]不详

出　　处：《应用数学和力学》2008年第5期575-588,共14页Applied Mathematics and Mechanics

基　　金：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);国家自然科学基金资助项目(10771124;10372052);国家教育部博士点基金资助项目(20030422047)

摘　　要：对非线性二相渗流耦合系统提出修正迎风分数步差分格式,利用变分形式、归纳法假定、高阶差分算子的分解、微分方程的先验估计理论和技巧,得到收敛性的最佳阶误差估计.该方法已成功应用于防治海水入侵主要工程后效预测与调控模式的生产实践中.For the three-dimensional nonlinear two-phase displacement problem, the modified upwind finite difference fractional steps schemes were put forward. Some techniques, such as calculus of variations, induction hypothesis, decomposition of high order difference operators, the theory of prior estimates and techniques were used. Optimal order estimates were derived for the error in the approximation solution. These methods have been successfully used in predicting the consequences of seawater intrusion and protection projects.

关 键 词：非线性偶合 迎风分数步 收敛性 海水入侵 后效和调控 

分 类 号：O241.82[理学—计算数学]