New paper: Enriched Galerkin finite elements for coupled poromechanics with local mass conservation

Our paper on enriched Galerkin finite element methods for coupled poromechanics, in collaboration with Prof. Sanghyun Lee at Florida State University, has been accepted for publication in Computer Methods in Applied Mechanics and Engineering.

Read the paper: Choo and Lee, CMAME 2018.

Abstract: Robust and efficient discretization methods for coupled poromechanical problems are critical to address a wide range of problems related to civil infrastructure, energy resources, and environmental sustainability. In this work, we propose a new finite element formulation for coupled poromechanical problems that ensures local (element-wise) mass conservation. The proposed formulation draws on the so-called enriched Galerkin method, which augments piecewise constant functions to the classical continuous Galerkin finite element method. These additional degrees of freedom allow us to obtain a locally conservative and nonconforming solution for the pore pressure field. The enriched and continuous Galerkin formulations are compared in several numerical examples ranging from a benchmark consolidation problem to a complex problem that involves plastic deformation due to unsaturated flow in a heterogeneous porous medium. The results of these examples show not only that the proposed method provides local mass conservation, but also that local mass conservation can be crucial to accurate simulation of deformation processes in fluid-infiltrated porous materials.

This work introduces enriched Galerkin (EG) finite element methods for locally mass conservative solution of coupled poromechanics problems. Shown above is EG solution of an unsaturated flow problem in a heterogeneous soil domain. Fluid mass is conserved locally (element-wise) in this pressure field. However, when the same problem is solved by the standard continuous Galerkin (CG) method, the simulation result is significantly different, and fluid mass shows nontrivial imbalances in many elements. This difference also impacts the deformation response of the problem.

This work introduces enriched Galerkin (EG) finite element methods for locally mass conservative solution of coupled poromechanics problems. Shown above is EG solution of an unsaturated flow problem in a heterogeneous soil domain. Fluid mass is conserved locally (element-wise) in this pressure field. However, when the same problem is solved by the standard continuous Galerkin (CG) method, the simulation result is significantly different, and fluid mass shows nontrivial imbalances in many elements. This difference also impacts the deformation response of the problem.