油气二次运移的LSQR迭代多重网格法及其应用

LSQR iterative multigrid method for sec ondary hydrocarbon migration and its application

本文给出了一种高效率求解油气二次运移偏微分方程的方法。该法是以水动力为油气运移模型，采用LSQR迭代、多重网格的加速计算方法。此法不仅极大地提高了油气二次运移偏微分方程的求解速度，而且可适用于不适定问题的求解。本文研究仍以二维油气运移模型为例，但其加速迭代的方法也完全适用于三维问题。此法的关键是从最细的网格出发．迭代求出近以解，然后在更粗的网格层上重复计算粗网格层的校正过程和光滑过程，最后在最粗网格层上准确求解残差方程。整个求解过程的计算量很小，内插和限制过程的工作量也很小。所以，此法可使现代大型计算机原先无法解决的三维油气二次运移模拟问题变成了可解问题。

An effective method for solving a partial differential equation of secondary hydrocarbon migration is put forward. The effective method involves water drive hydrocarbon migration model, multigrid and LSQR iteration. This method not onlygreatly speeds up solving a partial differential equation of secondary hydrocarbonmigration but also favours solving an ill posed problem. 2-D hydrocarbon migrationmodel is still taken as an example. but its fast iteration way is also applicable to 3-D problem.Essentially. the method starts from fine grid to iteratively obtain approximatesolution, then determines repeatedly the correction and smoothing procedures ofsparse grid l1aycr, followed by correctly solving the residual error equation on sparser grid layer. Less computation is needed in its solution, interpolation and restric-tion procedures. As a result, this method can be used to solve some tough 3-D hy-drocarbon secondary migration problems which could not be solved by modern largecomputers.