Review of the Application of Upwind Generalized Finite Difference Method in Two-Phase Fluid-Solid Coupling of Porous Media

Abstract

Porous media oil-water two-phase fluid-solid coupling is critical for oil-gas exploitation efficiency and environmental protection, but traditional mesh-based methods (FDM, FEM, FVM) suffer from mesh generation difficulties, poor dynamic adaptability, and numerical dissipation. The Generalized Finite Difference Method (GFDM), a promising meshless approach, offers a solution. This review synthesizes research progress on upwind GFDM in this coupling problem. It first sorts the evolution of porous media fluid-solid coupling theory (from Terzaghi’s to multi-physics extensions) and summarizes mesh-based/meshless methods, focusing on GFDM’s development and cross-field applications. It then analyzes how upwind-GFDM integration enhances convection-dominated flow stability/accuracy, addressing traditional meshless upwind challenges. Key gaps are identified: limited GFDM use in fractured porous media, unoptimized node layout/influence domains, and insufficient AI integration. Finally, the review concludes upwind GFDM provides a novel technical pathway for complex coupling problems, laying a foundation for meshless porous media simulators. It outlines future directions (fractured reservoir expansion, parameter optimization, AI fusion) to improve exploitation efficiency and environmental protection.

Keywords: Closed-loop optimization; History matching; Production optimization; Optimization algorithm

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