In the context of numerical simulators for multiphase flow in porous media, there exists a long‐standing issue known as the grid orientation effect (GOE), wherein different numerical solutions can be obtained when considering grids with different orientations under certain unfavorable conditions. The GOE is relevant to the instability near displacement fronts. If numerical oscillations accompanied by sharp fronts are not adequately suppressed, the GOE occurs. To reduce or even eliminate the GOE, we propose augmenting adaptive artificial viscosity in the process of solving the saturation equation. It has been demonstrated that appropriate artificial viscosity can effectively reduce or even eliminate the GOE. The proposed numerical method can be easily applied in practical engineering problems.

中文翻译：

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基于自适应人工黏度法的多孔介质两相流模拟中网格取向效应的数值策略


在多孔介质中多相流的数值模拟器中，存在一个长期存在的问题，称为网格取向效应 （GOE），即在某些不利条件下考虑具有不同取向的网格时，可以获得不同的数值解。GOE 与位移锋附近的不稳定性有关。如果伴随着尖锐锋面的数字振荡没有得到充分抑制，就会发生 GOE。为了减少甚至消除 GOE，我们建议在求解饱和方程的过程中增加自适应人工粘度。事实证明，适当的人工粘度可以有效降低甚至消除 GOE。所提出的数值方法可以方便地应用于实际工程问题中。