Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix–fracture interfaces
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- by Francesco Bonaldi, Jérôme Droniou and Roland Masson;
- Math. Comp. 93 (2024), 2103-2134
- DOI: https://doi.org/10.1090/mcom/3949
- Published electronically: March 7, 2024
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Abstract:
We present a complete numerical analysis for a general discretization of a coupled flow–mechanics model in fractured porous media, considering single-phase flows and including frictionless contact at matrix–fracture interfaces, as well as nonlinear poromechanical coupling. Fractures are described as planar surfaces, yielding the so-called mixed- or hybrid-dimensional models. Small displacements and a linear elastic behavior are considered for the matrix. The model accounts for discontinuous fluid pressures at matrix–fracture interfaces in order to cover a wide range of normal fracture conductivities.
The numerical analysis is carried out in the Gradient Discretization framework (see J. Droniou, R. Eymard, T. Gallouët, C. Guichard, and R. Herbin [The gradient discretisation method, Springer, Cham, 2018]), encompassing a large family of conforming and nonconforming discretizations. The convergence result also yields, as a by-product, the existence of a weak solution to the continuous model. A numerical experiment in 2D is presented to support the obtained result, employing a Hybrid Finite Volume scheme for the flow and second-order finite elements ($\mathbb {P}_2$) for the mechanical displacement coupled with face-wise constant ($\mathbb P_0$) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions.
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Bibliographic Information
- Francesco Bonaldi
- Affiliation: IMAG, Univ Montpellier, CNRS, Montpellier, France; and LAMPS, Université de Perpignan Via Domitia, Perpignan, France
- MR Author ID: 1019710
- ORCID: 0000-0003-0512-0362
- Email: francesco.bonaldi@univ-perp.fr
- Jérôme Droniou
- Affiliation: School of Mathematics, Monash University, Victoria 3800, Australia; and IMAG, Univ Montpellier, CNRS, Montpellier, France
- MR Author ID: 655312
- ORCID: 0000-0002-3339-3053
- Email: jerome.droniou@umontpellier.fr
- Roland Masson
- Affiliation: Université Côte d’Azur, Inria, CNRS, Laboratoire J.A. Dieudonné, team Coffee, Nice, France
- MR Author ID: 610229
- Email: roland.masson@univ-cotedazur.fr
- Received by editor(s): February 6, 2022
- Received by editor(s) in revised form: January 3, 2024, and January 21, 2024
- Published electronically: March 7, 2024
- Additional Notes: This work was partially funded by the European Union (ERC Synergy, NEMESIS, project number 101115663)
The first author is the corresponding author - © Copyright 2024 American Mathematical Society
- Journal: Math. Comp. 93 (2024), 2103-2134
- MSC (2020): Primary 65M12, 76S05, 74B10, 74M15
- DOI: https://doi.org/10.1090/mcom/3949
- MathSciNet review: 4759371