Enriched Galerkin Discretization for Modeling Poroelasticity and Permeability Alteration in Heterogeneous Porous Media

💡 Research Summary

This paper addresses the challenging problem of accurately simulating coupled fluid flow and solid deformation in heterogeneous porous media, where spatial variations in permeability and storage properties can be extreme. The authors adopt the Enriched Galerkin (EG) finite‑element method to discretize Biot’s poroelastic system, and they compare its performance against the classic continuous Galerkin (CG) and discontinuous Galerkin (DG) approaches.

The EG method is constructed by augmenting the standard continuous polynomial space for pressure with a piecewise‑constant function defined at the centre of each element. Formally, the pressure space is (P^{k}{\text{EG}} = P^{k}{\text{CG}} + P^{0}_{\text{DG}}). This enrichment retains the symmetric interior‑penalty bilinear form used in DG, guaranteeing local mass conservation, while requiring far fewer degrees of freedom (approximately one‑half to one‑third of DG in two‑ and three‑dimensional problems). The displacement field is kept in a standard CG space because the mechanical coefficients are assumed homogeneous.

Mathematically, the linear momentum balance is discretized with CG for the displacement, while the mass‑balance equation is discretized with EG for the pressure. The authors employ standard jump and weighted‑average operators on interior faces, and they introduce a harmonic average of the permeability tensor (\kappa) to handle strong heterogeneity. Permeability alteration due to volumetric strain is modeled by the relation
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