利用改进的ADI方法实现单机千万节点的油水两相渗流数值模拟

针对实际油藏的非均质分布特征及其复杂的边界条件，本文通过引入迭代参数的压缩因子和放大因子，对现有的交替方向迭代法(ADI)进行改进，提出一种适用于大规模油藏数值模拟的新算法．改进的ADI 方法计算精度可靠，且与现有的算法相比计算效率有所提高．更为关键的是，ADI 算法将求解三维压力方程的七对角矩阵分解为三个方向的三对角矩阵依次迭代求解，所需的运算存储量大幅减少，最大的计算规模有了大幅的提升．使用改进的ADI 方法，在单机上成功实现了千万节点的油水两相渗流数值模拟．计算实例表明，在同等单机硬件条件下，改进ADI 算法的最大计算规模是现有算法的1.7 倍以上．

Numerical Simulation of Oil-Water Two-Phase Flow with Ten Million Girds on Personal Computer by Using a Modified ADI Method

A modified ADI method is proposed in this article by introducing the compressibility and amplification factor of the iterative parameter of the original ADI method, in order to adapt to the strong heterogeneity and complex boundary conditions in practical numerical reservoir simulation. The simulation results of the proposed method are reliable and its efficiency is a little higher than the common methods. More importantly, the modified ADI method can save a lot of computer memory through decomposing the original seven-diagonal matrix into three tridiagonal ones and solving them iteratively. Ten million girds simulation for oil-water two-phase flow is realized on stand-alone computer by using the modified ADI method. Numerical examples show that the maximum grid number that the modified ADI method can afford on stand-alone computer, is 1.7 times bigger than the common methods.