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Numerische Mathematik

, Volume 141, Issue 1, pp 21–62 | Cite as

Numerical analysis of a two-phase flow discrete fracture matrix model

  • Jérôme Droniou
  • Julian HennickerEmail author
  • Roland Masson
Article

Abstract

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.

Mathematics Subject Classification

65M08 65M60 76M12 76M10 76S05 65M12 35K51 35K55 46N40 

Notes

Acknowledgements

The authors would like to thank Total S.A. and the Australian Research Council’s Discovery Projects funding scheme (Project Number DP170100605) for supporting this work.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jérôme Droniou
    • 1
  • Julian Hennicker
    • 2
    • 3
    Email author
  • Roland Masson
    • 2
  1. 1.School of Mathematical SciencesMonash UniversityVictoriaAustralia
  2. 2.Université Côte d’Azur, CNRS, Inria team COFFEE, LJADNiceFrance
  3. 3.Total SA, Centre scientifique et technique Jean-FégerPauFrance

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