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Pré-Publication, Document De Travail Année : 2022

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

Résumé

We present a complete numerical analysis for a general discretization of a coupled flowmechanics 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 [30], 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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Dates et versions

hal-03541096 , version 1 (24-01-2022)
hal-03541096 , version 2 (23-01-2024)

Identifiants

  • HAL Id : hal-03541096 , version 1

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Francesco Bonaldi, Jérôme Droniou, Roland Masson. Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix–fracture interfaces. 2022. ⟨hal-03541096v1⟩
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