三维渗流耦合系统动边值问题迎风差分方法的理论和应用

Theory and application of upwind finite difference method for moving boundary value problem of three-dimensional percolation coupled system

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两类迎风差分格式,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l^2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 multilayer dynamics of fluids in porous media, two kinds of upwind finite difference schemes applicable to parallel arithmetic are put 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. The estimates in 12 norm are derived to determine the error in the approximate solution. This method has already been applied to the numerical simulation of migration-accumulation of oil resources.