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文中用三种方法导出了微分算子(?)(a(?)p)在矩形网格上的九点差分近似的正确公式。使用它,在均质情况下,对拉普拉斯方程、布阿松方程和热传导方程可以构造出高阶精度的差分近似。因而认为在油藏数值模拟中遇到的非均质情况下,使用这种九点差分近似更为合理。文中指出了有关文献提出的矩形网格上的九点差分近似公式中的问题。
In this paper, we derive the correct formula of nine point difference approximation of differential operator (?) (A (?) P) on rectangular grid by three methods. Using it, under high-order conditions, Laplacian equations, Boussines’ equations, and heat conduction equations can be used to construct high-order differential approximations. Therefore, it is considered that it is more reasonable to use this nine-point difference approximation in the case of heterogeneity encountered in reservoir numerical simulation. The paper points out the problems in the nine-point difference approximation formula of the rectangular grid proposed by the literature.