【摘要】 针对三相黑油模型模拟时大规模对角稀疏线性方程组存储占用大量内存、求解耗时的问题,研究大规模稀疏系数矩阵的压缩存储及求解方法。提出了有效节点压缩和块压缩存储结合的压缩存储方法,以油藏节点为单元,利用3个实数组分别存储稀疏矩阵块主对角元素、下三角及上三角的非零块元素;由于模拟中形成的系数矩阵具有位置对称性,利用3个整型数组存储下三角非零块元素的地址信息,减少了内存损耗及运算中非零元素的搜索次数。在此基础上,采用Krylov子空间块广义极小余量GMRES迭代法结合块不完全LU预处理方法求解上述线性方程组。结果表明,解法收敛速度快、稳定性好,可以提高大型稀疏线性方程组的求解速度。经过黑油模型标准考题的测试证实,该方法能够有效求解大规模油藏数值模拟问题。更多还原

【Abstract】 The block compressed storage and solving methods in reservoir simulation are explored to resolve large sparse linear equations emerging in three-phase black oil model.In this paper,the active nodes are compressed firstly,and then the block main diagonal elements,nonzero block elements in lower triangular and upper triangular are separately stored into three real arrays.Owing to the coefficient matrix arising in the reservoir simulation being symmetrical,the addresses of block elements in lower triangular are deposited in three integer arrays.This block compressed storage method can save lots of memory and reduce the search frequencies of non-zero elements.On the basis of such compression storage,the block incomplete LU preconditioned generalized minimal residual method(GMRES) is adopted to solve the equations,showing that it is an effective method possessing fast convergence and good stability.Testing of black oil model example reveals that the block compressed storage and solving methods are effective in solving the large-scale reservoir simulation.更多还原