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

Eymard, 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 -