A Fully Coupled Monolithic Finite Element Framework for Pore-Scale Hydromechanical Processes in Porous Media
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At the microscopic scale of porous media, deformation of the solid skeleton alters pore geometry and effective flow pathways, thereby modifying intrinsic permeability, while pore fluid pressure simultaneously governs solid compression and stress redistribution. Capturing this bidirectional coupling is essential for providing physics-consistent parameters to macroscopic poromechanical models without resorting to phenomenological assumptions. In this study, a monolithic hydromechanical framework is proposed to simulate fluid flow and solid deformation in porous media at the pore scale. Fluid flow within the pore space is governed by the compressible Navier–Stokes equations, while the solid matrix is modeled using linear elasticity. To consistently account for the evolution of pore geometry induced by solid deformation, a diffusion-based mesh adaptation strategy is employed, enabling continuous and stable remeshing of the fluid domain. The governing equations are discretized using a fully implicit finite element formulation [1]. Equal-order interpolation for velocity and pressure is stabilized using the Pressure-Stabilized Petrov–Galerkin (PSPG) method. Periodic boundary conditions are imposed on representative volume elements to ensure accurate homogenization of effective mechanical properties. Fluid and solid interaction is enforced through kinematic compatibility and dynamic equilibrium at their interfaces. Configuration-dependent macroscopic stiffness tensors are obtained via a perturbation-based numerical homogenization approach and updated automatically as the microstructure evolves. The proposed monolithic hydromechanical model is fully integrated into an independently developed numerical simulator [2]. The model and its implementation are validated against a series of benchmark problems, including two-dimensional laminar flow around obstacles, Poiseuille flow, and three-dimensional Stokes flow past a sphere, and Terzaghi’s effective stress principle, with results showing excellent agreement with analytical solutions and reference data. Overall, the developed framework constitutes a robust and efficient computational tool for pore-scale hydromechanical analysis and provides a solid foundation for future multiscale modeling of coupled processes in porous materials.
