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

Jérôme Droniou, Julian Hennicker, Roland Masson

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

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.

Original languageEnglish
Pages (from-to)21–62
Number of pages42
JournalNumerische Mathematik
Volume141
Issue number1
DOIs
Publication statusPublished - Jan 2019

Cite this

Droniou, Jérôme ; Hennicker, Julian ; Masson, Roland. / Numerical analysis of a two-phase flow discrete fracture matrix model. In: Numerische Mathematik. 2019 ; Vol. 141, No. 1. pp. 21–62.
@article{048e5e5bf1da4c7d9e6280511619d8ce,
title = "Numerical analysis of a two-phase flow discrete fracture matrix model",
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.",
author = "J{\'e}r{\^o}me Droniou and Julian Hennicker and Roland Masson",
year = "2019",
month = "1",
doi = "10.1007/s00211-018-0994-y",
language = "English",
volume = "141",
pages = "21–62",
journal = "Numerische Mathematik",
issn = "0029-599X",
publisher = "Springer-Verlag London Ltd.",
number = "1",

}

Numerical analysis of a two-phase flow discrete fracture matrix model. / Droniou, Jérôme; Hennicker, Julian; Masson, Roland.

In: Numerische Mathematik, Vol. 141, No. 1, 01.2019, p. 21–62.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Numerical analysis of a two-phase flow discrete fracture matrix model

AU - Droniou, Jérôme

AU - Hennicker, Julian

AU - Masson, Roland

PY - 2019/1

Y1 - 2019/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85053441271&partnerID=8YFLogxK

U2 - 10.1007/s00211-018-0994-y

DO - 10.1007/s00211-018-0994-y

M3 - Article

VL - 141

SP - 21

EP - 62

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 1

ER -