Numerical analysis of a mixed-dimensional poromechanical model with frictionless contact at matrix-fracture interfaces
| Autor: | Bonaldi, Francesco, Droniou, Jérôme, Masson, Roland |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Mathematics of Computation, 2024 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1090/mcom/3949 |
| Popis: | 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. Comment: 30 pages, 9 figures |
| Databáze: | arXiv |
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