Krylov子空间投影法及其在油藏数值模拟中的应用

Krylov Subspace Projection Method and Its Application on Oil Reservoir Simulation

Krylov子空间投影法是一类非常有效的大型线性代数方程组解法 ,随着左右空间Lm、Km的不同选取可以得到许多人们熟知的方法· 按矩阵Hm 的不同类型 ,将Krylov子空间方法分成两大类 ,简要分析了这两类方法的优缺点及其最新进展 · 将目前最为可靠实用的广义最小余量法(GMRES)应用于油藏数值模拟计算问题 ,利用矩阵分块技术 ,采用块拟消去法 (PE)对系数阵进行预处理· 计算结果表明本文的预处理GMRES方法优于目前使用较多的预处理正交极小化ORTHMIN方法 ,最后还讨论了投影类方法的局限和今后的可能发展方向·

Krylov subspace projection methods are known to be highly efficient for solving large linear systems. Many different versions arise from different choices to the left and right subspaces. These methods were classified into two groups in terms of the different forms of matrix H m, the main properties in applications and the new versions of these two types of methods were briefly reviewed, then one of the most efficient versions, GMRES method was applied to oil reservoir simulation. The block Pseudo_Elinimation method was used to generate the preconditioned matrix. Numerical results show much better performance of this preconditioned techniques and the GMRES method than that of preconditioned ORTHMIN method, which is now in use in oil reservoir simulation. Finally, some limitations of Krylov subspace methods and some potential improvements to this type of methods are furtherly presented.