非线性渗流耦合系统动边值问题二阶迎风分数步差分方法  

The second-order upwind finite difference fractional steps method for moving boundary value problem of nonlinear percolation coupled system

作　　者：袁益让[1] 

机构地区：[1]山东大学数学研究所,济南250100

出　　处：《中国科学：数学》2012年第8期845-864,共20页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:10372052;10771124和11101244);山东省自然科学基金(批准号:ZR2009AQ012);山东大学自主创新基金(批准号:2010TS031)资助项目

摘　　要：对多层非线性渗流方程耦合系统三维动边值问题,提出适合并行计算的一类二阶迎风分数步差分格式,利用区域变换、变分形式、能量方法、隐显格式的相互结合、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 nonlinear coupled system with moving boundary values of multilayer dynamics of fluids in porous media, a kind of second-order upwind finite difference fractional steps schemes applicable to parallel arithmetic areput forward. Some techniques, such as the change of variables, calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates, are adopted. Optimal order estimates in 12 norm are derived to determine the error in the approximate solution. This method has Mready been applied to the numerical simulation of migration-accumulation of oil resources.

关 键 词：多层非线性渗流耦合 三维动边界 二阶迎风分数步差分 最佳阶l2估计 能源数值模拟 

分 类 号：O175.8[理学—数学]