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

Our paper on locally mass conservative finite element framework for large deformation poromechanics has been accepted for publication in International Journal for Numerical Methods in Engineering.

Read the paper: Choo, IJNME 2018.

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 (element-wise) 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 element-wise 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.

This paper proposes the first locally mass conservative finite element framework for large deformation poromechanical problems. The formulation builds on our previous work on enriched Galerkin (EG) methods. This figure shows local (element-wise) mass residuals in a synthetic land subsidence problem due to groundwater withdrawal. It can be seen that the local mass residuals are significant in the conventional continuous Galerkin (CG) solutions, but they become nearly zero in the EG solutions. This difference also affects the predicted subsidence results. The property of local mass conservation can become far more important once the flow is coupled with a transport phenomenon.

This paper proposes the first locally mass conservative finite element framework for large deformation poromechanical problems. The formulation builds on our previous work on enriched Galerkin (EG) methods. This figure shows local (element-wise) mass residuals in a synthetic land subsidence problem due to groundwater withdrawal. It can be seen that the local mass residuals are significant in the conventional continuous Galerkin (CG) solutions, but they become nearly zero in the EG solutions. This difference also affects the predicted subsidence results. The property of local mass conservation can become far more important once the flow is coupled with a transport phenomenon.