Numerical analysis of a two-phase flow discrete fracture model

Jérôme 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

We present a new model for two phase Darcy flows in fractured media, in which fractures are modelled as submanifolds of codimension one with respect to the surrounding domain (matrix). Fractures can act as drains or as barriers, since pressure discontinuities at the matrix-fracture interfaces are permitted. Additionally, a layer of damaged rock at the matrix-fracture interfaces is accounted for. The numerical analysis is carried out in the general framework of the Gradient Discretisation Method. Compactness techniques are used to establish convergence results for a wide range of possible numerical schemes; the existence of a solution for the two phase flow model is obtained as a byproduct of the convergence analysis. A series of numerical experiments conclude the paper, with a study of the influence of the damaged layer on the numerical solution.

Domaines: Analyse numérique [math.NA]

Jérôme Droniou, Julian Hennicker, Roland Masson. Numerical analysis of a two-phase flow discrete fracture model. 2016. ⟨hal-01422477v1⟩