渗流耦合系统动边值问题特征分数步差分方法  

Modified Characteristic Finite Difference Fractional Steps Method for Moving Boundary Value Problem of Percolation Coupled System

作　　者：袁益让[1] 李长峰[2] 孙同军 

机构地区：[1]山东大学数学研究所,济南250100 [2]山东大学经济学院,济南250100

出　　处：《应用数学和力学》2012年第2期177-194,共18页Applied Mathematics and Mechanics

基　　金：国家重点基础研究专项经费资助项目(19990328);国家攻关资助项目(20050200069);国家自然科学基金资助项目(10771124;10372052;11101244);教育部博士点基金资助项目(20030422047);山东省自然科学基金资助项目(ZR2009AQ012)

摘　　要：对多层渗流方程耦合系统动边值问题,提出适合并行计算的一类特征分数步差分格式,利用区域变换、变分形式、粗细网格配套、乘积型叁二次插值、差分算子乘积交换性、高阶差分算子的分解、先验估计的理论和技巧,得到收敛性的最佳阶l2误差估计.该方法已成功地应用到多层油资源运移聚集的资源评估生产实际中,得到了很好的数值模拟结果.For coupled system with moving boundary values of muitilayer dynamics of fluids in porous media, a kind of characteristic finite difference fractional steps scheme applicable to par- allel arithmetic were put forward. Some techniques, such as the change of regions, calculus of variations, piecewise threefold quadratic interpolation, muitiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, were adopted. Optimal order estimates in 12 norm are derived to determine the error in the ap- proximate solution. This method has already been applied to the numerical simulation of migra- tion-accumulation of oil resources.

关 键 词：多层渗流耦合 动边界 特征分数步差分 最佳阶误差估计 能源数值模拟 

分 类 号：O241.82[理学—计算数学]