Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces

Fuente: arXiv
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Autori principali: Bonaldi, Francesco, Droniou, Jérôme, Masson, Roland
Natura: Preprint
Pubblicazione: 2022
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author Bonaldi, Francesco
Droniou, Jérôme
Masson, Roland
author_facet Bonaldi, Francesco
Droniou, Jérôme
Masson, Roland
contents 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, 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.
format Preprint
id arxiv_https___arxiv_org_abs_2201_09646
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
Bonaldi, Francesco
Droniou, Jérôme
Masson, Roland
Numerical Analysis
65M12, 76S05, 74B10, 74M15
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, 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.
title Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
topic Numerical Analysis
65M12, 76S05, 74B10, 74M15
url https://arxiv.org/abs/2201.09646