# Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

Robert Eymard; Cindy Guichard; Raphaèle Herbin; Roland Masson

ESAIM: Proceedings (2012)

- Volume: 35, page 59-78
- ISSN: 1270-900X

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topEymard, Robert, et al. Denis Poisson, Fédération, and Trélat, E., eds. "Vertex centred Discretization of Two-Phase Darcy flows on General Meshes." ESAIM: Proceedings 35 (2012): 59-78. <http://eudml.org/doc/251274>.

@article{Eymard2012,

abstract = {This paper concerns the discretization of multiphase Darcy flows, in the case of
heterogeneous anisotropic porous media and general 3D meshes used in practice to represent
reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred
approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient
scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase
Darcy flows. The convergence of the VAG scheme is proved for a simplified two-phase Darcy
flow model, coupling an elliptic equation for the pressure and a linear hyperbolic
equation for the saturation. The ability for the VAG scheme to efficiently deal with
highly heterogeneous media and complex meshes is exhibited on immiscible and miscible two
phase Darcy flow models.},

author = {Eymard, Robert, Guichard, Cindy, Herbin, Raphaèle, Masson, Roland},

editor = {Denis Poisson, Fédération, Trélat, E.},

journal = {ESAIM: Proceedings},

keywords = {Finite volume; two phase Darcy flows; diffusion fluxes; general meshes; heterogeneous anisotropic media; finite volume},

language = {eng},

month = {4},

pages = {59-78},

publisher = {EDP Sciences},

title = {Vertex centred Discretization of Two-Phase Darcy flows on General Meshes},

url = {http://eudml.org/doc/251274},

volume = {35},

year = {2012},

}

TY - JOUR

AU - Eymard, Robert

AU - Guichard, Cindy

AU - Herbin, Raphaèle

AU - Masson, Roland

AU - Denis Poisson, Fédération

AU - Trélat, E.

TI - Vertex centred Discretization of Two-Phase Darcy flows on General Meshes

JO - ESAIM: Proceedings

DA - 2012/4//

PB - EDP Sciences

VL - 35

SP - 59

EP - 78

AB - This paper concerns the discretization of multiphase Darcy flows, in the case of
heterogeneous anisotropic porous media and general 3D meshes used in practice to represent
reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred
approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient
scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase
Darcy flows. The convergence of the VAG scheme is proved for a simplified two-phase Darcy
flow model, coupling an elliptic equation for the pressure and a linear hyperbolic
equation for the saturation. The ability for the VAG scheme to efficiently deal with
highly heterogeneous media and complex meshes is exhibited on immiscible and miscible two
phase Darcy flow models.

LA - eng

KW - Finite volume; two phase Darcy flows; diffusion fluxes; general meshes; heterogeneous anisotropic media; finite volume

UR - http://eudml.org/doc/251274

ER -

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