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

TL;DR

This paper introduces an adaptive artificial viscosity method to mitigate the grid orientation effect in two-phase flow simulations in porous media, improving numerical stability and accuracy near displacement fronts.

Contribution

The paper proposes a novel adaptive artificial viscosity approach to effectively reduce grid orientation effects in multiphase flow simulations.

Findings

Artificial viscosity reduces spurious oscillations.

Method effectively mitigates grid orientation effects.

Applicable to practical engineering problems.

Abstract

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.