# Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 5, page 973-1001
- ISSN: 0764-583X

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topCancès, Clément. "Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 973-1001. <http://eudml.org/doc/250661>.

@article{Cancès2009,

abstract = {
We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can
be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions.
We approximate the solution of our problem thanks to a monotonous finite volume scheme. The convergence of the underlying discrete solution
to a weak solution when the discretization step tends to 0 is then proven. We also show, under assumptions on the initial data, a uniform estimate on the flux, which is then used during the uniqueness proof. A density argument allows us to relax the assumptions on the initial data and to extend the existence-uniqueness frame to
a family of solution obtained as limit of approximations. A numerical example is then given to illustrate the behavior of the model.
},

author = {Cancès, Clément},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Capillarity discontinuities; degenerate parabolic equation; finite volume scheme; convergence; uniqueness; existence},

language = {eng},

month = {8},

number = {5},

pages = {973-1001},

publisher = {EDP Sciences},

title = {Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities},

url = {http://eudml.org/doc/250661},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Cancès, Clément

TI - Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2009/8//

PB - EDP Sciences

VL - 43

IS - 5

SP - 973

EP - 1001

AB -
We study a one-dimensional model for two-phase flows in heterogeneous media, in which the capillary pressure functions can
be discontinuous with respect to space. We first give a model, leading to a system of degenerated nonlinear parabolic equations spatially coupled by nonlinear transmission conditions.
We approximate the solution of our problem thanks to a monotonous finite volume scheme. The convergence of the underlying discrete solution
to a weak solution when the discretization step tends to 0 is then proven. We also show, under assumptions on the initial data, a uniform estimate on the flux, which is then used during the uniqueness proof. A density argument allows us to relax the assumptions on the initial data and to extend the existence-uniqueness frame to
a family of solution obtained as limit of approximations. A numerical example is then given to illustrate the behavior of the model.

LA - eng

KW - Capillarity discontinuities; degenerate parabolic equation; finite volume scheme; convergence; uniqueness; existence

UR - http://eudml.org/doc/250661

ER -

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