Hybrid Finite Volume discretization of two-phase Discrete Fracture Matrix models with nonlinear interface solver

Aghili, Joubine; Brenner, Konstantin; Hennicker, Julian; Masson, Roland; Trenty, Laurent

doi:10.3997/2214-4609.201802272

Cited by 7 publications

(13 citation statements)

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“…Improving the numerical efficiency for this type of DFM models is the object of ongoing researches in two directions. The first is to go back to face based discretizations allowing the elimination of the mf interface unknowns with a local nonlinear interface solver as in [1] using TPFA discretization on orthogonal meshes and in [2] using an HFV discretization. The second perspective is to use the more robust Hybrid Upwinding approximation of the mobilities to define the two-phase Darcy fluxes at mf interfaces as proposed in [6] for TPFA schemes and in [19] for the VAG discretization.…”

Section: Discussionmentioning

confidence: 99%

“…The last type of models considers nonlinear mf transmission conditions which are based on the nonlinear (including mobility) two-phase normal flux continuity equations at mf interfaces. This type of models is considered in [16,25,2,1,6] using a two-point flux approximation in the fracture width with upwinding of the mobilities, and in [40,3] using a global pressure formulation. Such nonlinear transmission conditions account for the discontinuity of both the phase pressures and the mobilities at mf interfaces.…”

Section: Introductionmentioning

confidence: 99%

“…Alternatively, cell centred discretizations have been considered for DFM two-phase flow models using the Two-Point Flux Approximation (TPFA) as in [41,1,6] or Multi-Point Flux Approximations (MPFA) as in [36,5,52]. Face based discretizations have been considered in [38,3] using the Mixed Hybrid Finite Element (MHFE) method and in [37,2] using the Hybrid Finite Volume (HFV) scheme. Non conforming discretizations have also been developed for this type of models using XFEM discretizations as in [34] or Embedded Discrete Fracture Models as in [50].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nodal Discretization of Two-Phase Discrete Fracture Matrix Models

Brenner

Hennicker

Masson

2021

Polyhedral Methods in Geosciences

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nodal Discretization of Two-Phase Discrete Fracture Matrix Models

Brenner

Hennicker

Masson

2021

Polyhedral Methods in Geosciences

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“…The Fickian diffusion in the gas phase and in the fracture width is shown to remove the barrier effect induced by the gas filled fractures. In perspective, the discretization will be extended to account for general meshes and anisotropy of the permeability tensor using a face based approach in the spirit of [52].…”

Section: Discussionmentioning

confidence: 99%

A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

Aghili

Dreuzy

Masson

et al. 2021

Journal of Computational Physics

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“…It results that the mf nonlinear model combined with the VAG discretization exhibits a large computational overhead compared with the continuous pressure model. To extend the elimination of the mf interface unknowns to consistent discretizations on general meshes, a promising approach developped in [1] is to use face-based discretizations [8] rather than nodal-based discretizations.…”

Section: D Numerical Experimentsmentioning

confidence: 99%

Two-phase Discrete Fracture Matrix models with linear and nonlinear transmission conditions

et al. 2019

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This work deals with two-phase Discrete Fracture Matrix models coupling the two-phase Darcy flow in the matrix domain to the two-phase Darcy flow in the network of fractures represented as co-dimension one surfaces. Two classes of such hybrid-dimensional models are investigated either based on nonlinear or linear transmission conditions at the matrix-fracture interfaces. The linear transmission conditions include the cell-centred upwind approximation of the phase mobilities classically used in the porous media flow community as well as a basic extension of the continuous phase pressure model accounting for fractures acting as drains. The nonlinear transmission conditions at the matrix-fracture interfaces are based on the normal flux continuity equation for each phase using additional interface phase pressure unknowns. They are compared both in terms of accuracy and numerical efficiency to a reference equi-dimensional model for which the fractures are represented as full-dimensional subdomains. The discretization focuses on Finite Volume cellcentred Two-Point Flux Approximation which is combined with a local nonlinear solver allowing to eliminate efficiently the additional matrix-fracture interfacial unknowns together with the nonlinear transmission conditions. 2D numerical experiments illustrate the better accuracy provided by the nonlinear transmission conditions compared to their linear approximations with a moderate computational overhead obtained thanks to the local nonlinear elimination at the matrix-fracture interfaces. The numerical section is complemented by a comparison of the reduced models on a 3D test case using the Vertex Approximate Gradient scheme.

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Hybrid Finite Volume discretization of two-phase Discrete Fracture Matrix models with nonlinear interface solver

Cited by 7 publications

References 0 publications

Nodal Discretization of Two-Phase Discrete Fracture Matrix Models

Nodal Discretization of Two-Phase Discrete Fracture Matrix Models

A hybrid-dimensional compositional two-phase flow model in fractured porous media with phase transitions and Fickian diffusion

Two-phase Discrete Fracture Matrix models with linear and nonlinear transmission conditions

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