A comparative study of fine-scale and multi-scale finite-volume and finite-element methods for coupled poroelastic problems

Abstract

Coupled geomechanical deformation and fluid flow phenomena arise in a wide range of subsurface processes, such as reservoir compaction, subsidence, and fault reactivation. Accurate and efficient simulation of these phenomena requires robust and consistent numerical formulations capable of capturing hydro-mechanical (HM) behavior in porous media. This study presents a detailed comparative numerical investigation of the multiscale finite-volume (MSFV) and multiscale finite-element (MSFE) formulations for fully coupled poroelastic problems. Both formulations are developed within a unified multiscale framework employing local basis functions, along with restriction and prolongation operators, to ensure consistent transfer of information between fine and coarse grids. The governing Biot equations, incorporating the balance of linear momentum and fluid mass, are solved in a fully implicit manner to achieve stable hydro-mechanical coupling. The MSFV formulation is based on a conservative staggered-grid discretization that guarantees local mass and stress conservation, whereas the MSFE approach utilizes continuous Galerkin (CG) interpolation providing smooth displacement and pressure fields. Performance, stability, and computational efficiency are assessed through benchmark problems, including Terzaghi’s consolidation, Mandel’s problem, and a heterogeneous permeability test. Our results indicate that both formulations accurately reproduce fine-scale reference solutions, while a hybrid discretization combining finite elements for displacement and finite volume for pressure delivers the most favorable balance between accuracy, stability, and conservation.