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It is a challenge to numerically solve nonlinear partial differentialequations whose solution involves discontinuity. In the context of numericalsimulators for multi-phase flow in porous media, there exists a long-standingissue known as Grid Orientation Effect (GOE), wherein different numericalsolutions can be obtained when considering grids with different orientationsunder certain unfavorable conditions. Our perspective is that GOE arises due tonumerical instability near displacement fronts, where spurious oscillationsaccompanied by sharp fronts, if not adequately suppressed, lead to GOE. Toreduce or even eliminate GOE, we propose augmenting adaptive artificialviscosity when solving the saturation equation. It has been demonstrated thatappropriate artificial viscosity can effectively reduce or even eliminate GOE.The proposed numerical method can be easily applied in practical engineeringproblems.

Numerical strategy on the grid orientation effect in the simulation for  two-phase flow in porous media by using the adaptive artificial viscosity  method