PEBI网格节点编号优化方法研究

基于PEBI网格的油藏数值模拟能够更准确地模拟地下油藏流动，模拟过程中主要是求解以PEBI网格为差分单元的有限差分方程。提出采用谱算法优化PEBI网格节点的编号来减少差分方程中系数矩阵的带宽，以节约计算时间和数据存储量。首先计算网格按初始编号所形成的邻接矩阵及其Laplacian矩阵，然后通过计算Laplacian矩阵的特征值和特征向量得到Fiedler特征向量，最后对Fiedler特征向量进行排序，并根据排序后的向量对PEBI重新编号。最后通过实验验证了谱算法在PEBI网格编号优化中的有效应用。

Research on optimization of numbering of PEBI grid node

The reservoir simulation based on PEBI grid can simulate more accurately.Its major calculation is to solve the finite difference equation which is based on the PEBI grid.In order to speed up the process and minimize the data storage,a method to optimize the numbering of PEBI grid through the spectral algorithm is presented,which can minimize the bandwidth of matrix which represents the finite difference equation＇s coefficient.There are three main steps in this algorithm.First, calculate the adjacent matrix of the grid and its Laplacian matrix in accordance with the original numbering.Then,get the Fiedler vector by computing the eigenvalues and eigenvectors of the Laplacian matrix.At last,sort the Fiedler vector through the quick sort,and renumber the grids according to the sorted Fiedler vector.In the end,the good result of PEBI grid＇s num-bering optimization through spectral algorithm is proved by experiment.