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

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, 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.

arXiv comment30 pages, 9 figures

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Cited by in corpus (2)

• A block preconditioner for thermo-poromechanics with frictional deformation of fractures
• An efficient preconditioner for mixed-dimensional contact poromechanics based on the fixed stress splitting scheme