  It is a challenge to numerically solve nonlinear partial differential
equations whose solution involves discontinuity. In the context of numerical
simulators for multi-phase flow in porous media, there exists a long-standing
issue known as Grid Orientation Effect (GOE), wherein different numerical
solutions can be obtained when considering grids with different orientations
under certain unfavorable conditions. Our perspective is that GOE arises due to
numerical instability near displacement fronts, where spurious oscillations
accompanied by sharp fronts, if not adequately suppressed, lead to GOE. To
reduce or even eliminate GOE, we propose augmenting adaptive artificial
viscosity when solving the saturation equation. It has been demonstrated that
appropriate artificial viscosity can effectively reduce or even eliminate GOE.
The proposed numerical method can be easily applied in practical engineering
problems.
