In this paper, we propose an analysis method for the so-called grid orientation effect (GOE) in the numerical simulation of two-phase flows in porous media. The GOE, which occurs when using coupled finite volume schemes on structured grids, is well known to engineers. Several attempts, most of which are of empirical nature, have been put forward in order to alleviate this undesirable phenomenon. Here, our approach relies on a more rigorous notion of angular error for all directions, which in turn enables us —via integration and minimization— to single out the “least anisotropic” scheme within a given family of schemes depending on some tuning parameter(s). Numerical test problems testify to the improvement brought by the new construction.

在本文中，我们提出了一种在多孔介质中两相流数值模拟中所谓的网格定向效应（GOE）的分析方法。工程师众所周知，在结构化网格上使用耦合有限体积方案时会发生GOE。为了减轻这种不良现象，已经提出了几种尝试，其中大多数是经验性的。在这里，我们的方法依赖于所有方向上更严格的角度误差概念，这又使我们能够（通过积分和最小化）根据某些调整参数，在给定的方案系列中选择“最小各向异性”方案）。数值测试问题证明了新结构带来的改进。