  We consider a two-phase Darcy flow in a fractured porous medium consisting in
a matrix flow coupled with a tangential flow in the fractures, described as a
network of planar surfaces. This flow model is also coupled with the mechanical
deformation of the matrix assuming that the fractures are open and filled by
the fluids, as well as small deformations and a linear elastic constitutive
law. The model is discretized using the gradient discretization method [26],
which covers a large class of conforming and non conforming schemes. This
framework allows for a generic convergence analysis of the coupled model using
a combination of discrete functional tools. Here, we describe the model
together with its numerical discretization, and we prove a convergence result
assuming the non-degeneracy of the phase mobilities and that the discrete
solutions remain physical in the sense that, roughly speaking, the porosity
does not vanish and the fractures remain open. This is, to our knowledge, the
first convergence result for this type of models taking into account two-phase
flows in fractured porous media and the non-linear poromechanical coupling.
Previous related works consider a linear approximation obtained for a single
phase flow by freezing the fracture conductivity [36, 37]. Numerical tests
employing the Two-Point Flux Approximation (TPFA) finite volume scheme for the
flows and $\mathbb P_2$ finite elements for the mechanical deformation are also
provided to illustrate the behavior of the solution to the model.
