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<p>In this paper, we introduce a novel physics-preserving multiscale approach to tackle the challenge of immiscible two-phase flow problems. These are typically described as a coupled system comprising Darcy’s law and mass conservation equations. Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme, is designed to uphold local mass conservation for both phases while remaining unbiased. Notably, when the time step is kept below a certain threshold, the P-IMPES scheme ensures bounds-preserving saturation for both phases. For velocity updates, we employ the mixed generalized multiscale finite element method (MGMsFEM), a highly efficient solver that operates on a coarse grid to compute unknowns. We adopt an operation splitting technique to manage the complexities of two-phase flow, utilizing an upwind strategy for explicit saturation iteration, while employing the MGMsFEM to compute velocity via a decoupled system on a coarse mesh. To validate the effectiveness and robustness of our proposed method, we conduct a series of comprehensive experiments. Additionally, we provide a rigorous analysis to establish the theoretical underpinnings of the method, which are corroborated by our numerical findings. Both simulations and analysis demonstrate that our approach strikes a favorable balance between accuracy and computational efficiency.</p>

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Physics-Preserving IMPES Based Multiscale Methods for Immiscible Two-Phase Flow in Highly Heterogeneous Porous Media

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月3日

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  • Yiran Wang,
  • Eric Chung,
  • Shuyu Sun

摘要

In this paper, we introduce a novel physics-preserving multiscale approach to tackle the challenge of immiscible two-phase flow problems. These are typically described as a coupled system comprising Darcy’s law and mass conservation equations. Physics-preserving IMplicit Pressure Explicit Saturation (P-IMPES) scheme, is designed to uphold local mass conservation for both phases while remaining unbiased. Notably, when the time step is kept below a certain threshold, the P-IMPES scheme ensures bounds-preserving saturation for both phases. For velocity updates, we employ the mixed generalized multiscale finite element method (MGMsFEM), a highly efficient solver that operates on a coarse grid to compute unknowns. We adopt an operation splitting technique to manage the complexities of two-phase flow, utilizing an upwind strategy for explicit saturation iteration, while employing the MGMsFEM to compute velocity via a decoupled system on a coarse mesh. To validate the effectiveness and robustness of our proposed method, we conduct a series of comprehensive experiments. Additionally, we provide a rigorous analysis to establish the theoretical underpinnings of the method, which are corroborated by our numerical findings. Both simulations and analysis demonstrate that our approach strikes a favorable balance between accuracy and computational efficiency.