Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model

J. Droniou, J. Hennicker, R Masson

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

1 Citation (Scopus)

Abstract

Flow and transport in fractured porous 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.

Original languageEnglish
Title of host publicationFinite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017
EditorsClément Cancès, Pascal Omnes
Place of PublicationCham Switzerland
PublisherSpringer
Pages275-283
Number of pages9
Volume199
ISBN (Electronic)9783319573977
ISBN (Print)9783319573960
DOIs
Publication statusPublished - 2017
EventFinite Volumes for Complex Applications 2017 - Université Lille 1, Lille, France
Duration: 12 Jun 201716 Jun 2017
Conference number: 8th
https://indico.math.cnrs.fr/event/1299/overview

Publication series

NameSpringer Proceedings in Mathematics & Statistics
PublisherSpringer International Publishing
Volume199
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

ConferenceFinite Volumes for Complex Applications 2017
Abbreviated titleFVCA 8
CountryFrance
CityLille
Period12/06/1716/06/17
OtherTheme = Hyperbolic, Elliptic and Parabolic Problems
Internet address

Keywords

  • Discrete fracture model
  • Gradient discretization method
  • Two-phase Darcy flow
  • Uniform-in-time convergence

Cite this

Droniou, J., Hennicker, J., & Masson, R. (2017). Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model. In C. Cancès, & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017 (Vol. 199, pp. 275-283). (Springer Proceedings in Mathematics & Statistics; Vol. 199). Cham Switzerland: Springer. https://doi.org/10.1007/978-3-319-57397-7_20
Droniou, J. ; Hennicker, J. ; Masson, R. / Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model. Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. editor / Clément Cancès ; Pascal Omnes. Vol. 199 Cham Switzerland : Springer, 2017. pp. 275-283 (Springer Proceedings in Mathematics & Statistics).
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Droniou, J, Hennicker, J & Masson, R 2017, Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model. in C Cancès & P Omnes (eds), Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. vol. 199, Springer Proceedings in Mathematics & Statistics, vol. 199, Springer, Cham Switzerland, pp. 275-283, Finite Volumes for Complex Applications 2017, Lille, France, 12/06/17. https://doi.org/10.1007/978-3-319-57397-7_20

Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model. / Droniou, J.; Hennicker, J.; Masson, R.

Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. ed. / Clément Cancès; Pascal Omnes. Vol. 199 Cham Switzerland : Springer, 2017. p. 275-283 (Springer Proceedings in Mathematics & Statistics; Vol. 199).

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

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Droniou J, Hennicker J, Masson R. Uniform-in-time convergence of numerical schemes for a two-phase discrete fracture model. In Cancès C, Omnes P, editors, Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017. Vol. 199. Cham Switzerland: Springer. 2017. p. 275-283. (Springer Proceedings in Mathematics & Statistics). https://doi.org/10.1007/978-3-319-57397-7_20