• Corpus ID: 246240370

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

@article{Bonaldi2022NumericalAO,
  title={Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces},
  author={Francesco Bonaldi and J{\'e}r{\^o}me Droniou and Roland Masson},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.09646}
}

• F. Bonaldi, J. Droniou, R. Masson
• Published 24 January 2022
• Mathematics
• ArXiv

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 mixedor 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 (P2) for the mechanical displacement coupled with face-wise constant (P0) Lagrange multipliers on fractures, representing normal stresses, to discretize the contact conditions. MSC2010: 65M12, 76S05, 74B10, 74M15