Uniform-in-Time Convergence of Numerical Schemes for a Two-Phase Discrete Fracture Model

Jerome Droniou (1) , Julian Hennicker (2, 3, 4) , Roland Masson (3, 4)

1 School of Mathematical Sciences [Clayton]
2 CSTJF - Centre scientifique et Technique Jean Feger
3 COFFEE - COmplex Flows For Energy and Environment
4 LJAD - Laboratoire Jean Alexandre Dieudonné

Flow and transport in fracturedporous media are of paramount importance for many applications such as petroleum exploration and production, geological storage of carbon dioxide, hydrogeology, or geothermal energy. We consider here the two-phase discrete fracture model introduced in [3] which represents explicitly the fractures as codimension one surfaces immersed in the surrounding matrix domain. Then, the two-phase Darcy flow in the matrix is coupled with the two-phase Darcy flow in the fractures using transmission conditions accounting for fractures acting either as drains or barriers. The model takes into account complex networks of fractures, discontinuous capillary pressure curves at the matrix fracture interfaces and can be easily extended to account for gravity including in the width of the fractures. It also includes a layer of damaged rock at the matrix fracture interface with its own mobility and capillary pressure functions. In this work, the convergence analysis carried out in [3] in the framework of gradient discretizations [2] is extended to obtain the uniform-in-time convergence of the discrete solutions to a weak solution of the model.

Mots clés: Two-phase Darcy flow; Uniform-in-time convergence; Gradient discretization method; Discrete fracture model

Domaines: Analyse numérique [math.NA]

Jerome Droniou, Julian Hennicker, Roland Masson. Uniform-in-Time Convergence of Numerical Schemes for a Two-Phase Discrete Fracture Model. FVCA 2017 - International Conference on Finite Volumes for Complex Applications VIII, Jun 2017, Lille, France. ⟨10.1007/978-3-319-57397-7_20⟩. ⟨hal-01541150⟩