非线性多层渗流系统的数值方法及其应用

Numerical Method and Application for the Three-Dimensional Nonlinear System of Dynamics of Fluids in Porous Media

对多层非线性渗流系统提出适合并行计算的迎风分数步差分格式,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、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到油资源渗流力学运移聚集数值模拟的生产实际中.

For the system of multilayer dynamics of fluids in porous media, the second order upwind finite difference fractional steps schemes applicable to parallel arithmetic are put forward. Some techniques, such as calculus of variations, energy method, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates were adopted. Optimal order estimates were 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.