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.

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.

EMI 2018 & Computational Mechanics Committee

Jinhyun Choo has attended the EMI 2018 Conference and delivered a talk entitled "Coupling phase-field and plasticity for unified modeling of brittle and ductile failures in geomaterials." He also co-chaired the Computational Geomechanics mini-symposium, which hosted a number of high-quality presentations. 

During the conference, Jinhyun has also been elected to be a member of the Computational Mechanics Committee. The purpose of the EMI Computational Mechanics Committee is to foster the development and applications of the methods of computational methods (finite element, boundary element, finite difference, finite volume, and others) to problems of engineering mechanics, including structural mechanics, solid mechanics, geomechanics, fluid mechanics, fluid–structure interaction, as well as dynamic and thermal effects.

EMI Poromechanics Committee

Jinhyun Choo has been elected to be a member of the Poromechanics Committee of the Engineering Mechanics Institute (EMI). EMI's technical committees develop conference sessions and symposia for Institute and Society conferences and for other initiatives to foster technical activities within the area of engineering mechanics. The purpose of the EMI Poromechanics Committee is to promote fundamental and applied research in the mechanics of porous materials using observational, analytical, and computational techniques.

Prof. Michael Celia from Princeton University visited us

We enjoyed this morning very much having a meeting with Prof. Michael Celia, the Director of Princeton Environmental Institute, the Theodora Shelton Pitney Professor of Environmental Studies, and a Professor of Civil and Environmental Engineering at Princeton University. We presented our recent and ongoing work at the interface of geomechanics and subsurface hydrology, and received invaluable comments and suggestions from him.

We are very grateful to Prof. Celia for visiting us during his one day stay in Hong Kong. We look forward to continuing interactions with him.

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