Large deformation poromechanics with local mass conservation: An enriched Galerkin finite element framework

Abstract

Numerical modeling of large deformations in fluid-infiltrated porous media must accurately describe not only geometrically nonlinear kinematics but also fluid flow in heterogeneously deforming pore structure. Accurate simulation of fluid flow in heterogeneous porous media often requires a numerical method that features the local (elementwise) conservation property. Here, we introduce a new finite element framework for locally mass conservative solution of coupled poromechanical problems at large strains. At the core of our approach is the enriched Galerkin discretization of the fluid mass balance equation, whereby elementwise constant functions are augmented to the standard continuous Galerkin discretization. The resulting numerical method provides local mass conservation by construction with a usually affordable cost added to the continuous Galerkin counterpart. Two equivalent formulations are developed using total Lagrangian and updated Lagrangian approaches. The local mass conservation property of the proposed method is verified through numerical examples involving saturated and unsaturated flow in porous media at finite strains. The numerical examples also demonstrate that local mass conservation can be a critical element of accurate simulation of both fluid flow and large deformation in porous media. KEYWORDS finite element method, enriched Galerkin method, poromechanics, large deformation, local mass conservation 66

Phase‐field modeling of rock fractures with roughness

“…We evaluate the shear stress and dilation of the cracks at quadrature points closest to the discontinuities. We obtain the numerical results from our in-house finite element code Geocentric, which is built on the open source finite element library deal.II 61 and has been used in a number of previous studies (e.g., [62][63][64][65] ).…”

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