2018
DOI: 10.1007/s00211-018-0994-y
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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 te… Show more

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Cited by 19 publications
(55 citation statements)
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“…Using (75) for the consistency term in m T pp u T , v T q (see (20)), plugging the resulting relation into the expression of a ξ h pp u h , v h q (see (26)), and accounting for (70) in the fracture terms of a ξ h pp u h , v h q (where π k F can be cancelled using (9) after observing that λ ξ F rrv h ss F P P k pF q and λ F rrv h ss F P P k pF q for all F P F Γ h ) gives (66).…”
mentioning
confidence: 99%
“…Using (75) for the consistency term in m T pp u T , v T q (see (20)), plugging the resulting relation into the expression of a ξ h pp u h , v h q (see (26)), and accounting for (70) in the fracture terms of a ξ h pp u h , v h q (where π k F can be cancelled using (9) after observing that λ ξ F rrv h ss F P P k pF q and λ F rrv h ss F P P k pF q for all F P F Γ h ) gives (66).…”
mentioning
confidence: 99%
“…We give here a brief overview of the notations, and refer to [3] for more details. Ω is a bounded polytopal domain of R d (d = 2, 3), partitioned into a fracture domain Γ and a matrix domain Ω \Γ .…”
Section: Continuous Modelmentioning
confidence: 99%
“…Under the assumptions of Section 1, let (D l ) l∈N be a coercive, consistent, limit-conforming and compact sequence of space-time GD (see [3]), and let (u α,l ) l∈N be such that u α,l ∈ (X 0 l ) N l +1 is a sequence of solutions of (3) with D = D l . Then, there exists a weak solution (u α m , u α f ) α=1,2 of the model such that, for all µ ∈ {m, f } and a ∈ χ,…”
Section: Definition 1 (Weak Solution Of the Model) A Weak Solution Omentioning
confidence: 99%
See 1 more Smart Citation
“…for linear and non-linear elliptic and parabolic diffusion equations (including degenerate equations), the Navier-Stokes equations, variational inequalities, Darcy flows in fractured media, etc. See for example [16,17,18,1,22], and the monograph [15] for a complete presentation of the GDM. The contributions of this article are summarised now.…”
Section: Introductionmentioning
confidence: 99%