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We consider a two-phase Darcy flow in a fractured and deformable porousmedium for which the fractures are described as a network of planar surfacesleading to so-called hybrid-dimensional models. The fractures are assumed openand filled by the fluids and small deformations with a linear elasticconstitutive law are considered in the matrix. As opposed to [10], the phasepressures are not assumed continuous at matrix fracture interfaces, whichraises new challenges in the convergence analysis related to the additionalinterfacial equations and unknowns for the flow. As shown in [16, 2], unlikesingle phase flow, discontinuous pressure models for two-phase flows provide abetter accuracy than continuous pressure models even for highly permeablefractures. This is due to the fact that fractures fully filled by one phase canact as barriers for the other phase, resulting in a pressure discontinuity atthe matrix fracture interface. The model is discretized using the gradientdiscretization method [22], which covers a large class of conforming and nonconforming schemes. This framework allows for a generic convergence analysis ofthe coupled model using a combination of discrete functional tools. In thiswork, the gradient discretization of [10] is extended to the discontinuouspressure model and the convergence to a weak solution is proved. Numericalsolutions provided by the continuous and discontinuous pressure models arecompared on gas injection and suction test cases using a Two-Point FluxApproximation (TPFA) finite volume scheme for the flows and $P_2$ finiteelements for the mechanics.

Gradient discretization of two-phase poro-mechanical models with discontinuous pressures at matrix fracture interfaces