Numerical Strategy on the Grid Orientation Effect in the Simulation for Two‐Phase Flow in Porous Media by Using the Adaptive Artificial Viscosity Method

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.