# Asymptotic and numerical modelling of flows in fractured porous media

Philippe Angot; Franck Boyer; Florence Hubert

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

- Volume: 43, Issue: 2, page 239-275
- ISSN: 0764-583X

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topAngot, Philippe, Boyer, Franck, and Hubert, Florence. "Asymptotic and numerical modelling of flows in fractured porous media." ESAIM: Mathematical Modelling and Numerical Analysis 43.2 (2009): 239-275. <http://eudml.org/doc/250659>.

@article{Angot2009,

abstract = {
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale,
so that we can asymptotically reduce them to immersed polygonal fault
interfaces and the model finally consists in a coupling between a
2D elliptic problem and a 1D equation on the sharp interfaces modelling the fractures.
A cell-centered finite volume scheme on general polygonal meshes fitting the interfaces
is derived to solve the set of equations with the additional
differential transmission conditions linking both pressure and normal velocity
jumps through the interfaces.
We prove the convergence of the FV scheme for any set of data and parameters of the models and derive existence and uniqueness of the solution to the asymptotic models proposed.
The models are then numerically experimented for highly or partially immersed fractures.
Some numerical results are reported showing different kinds of flows
in the case of impermeable or partially/highly permeable fractures.
The influence of the variation of the aperture of the fractures is also investigated. The numerical
solutions of the asymptotic models are validated by comparing them to the solutions of the global Darcy model or to some analytic solutions.
},

author = {Angot, Philippe, Boyer, Franck, Hubert, Florence},

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

keywords = {Fractured porous media; Darcy flow; finite volume method; asymptotic models of flow.; global solvability; cell-centered finite volume scheme; convergence; double-permeability model},

language = {eng},

month = {2},

number = {2},

pages = {239-275},

publisher = {EDP Sciences},

title = {Asymptotic and numerical modelling of flows in fractured porous media},

url = {http://eudml.org/doc/250659},

volume = {43},

year = {2009},

}

TY - JOUR

AU - Angot, Philippe

AU - Boyer, Franck

AU - Hubert, Florence

TI - Asymptotic and numerical modelling of flows in fractured porous media

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2009/2//

PB - EDP Sciences

VL - 43

IS - 2

SP - 239

EP - 275

AB -
This study concerns some asymptotic models used to compute the flow outside and inside fractures in a bidimensional porous medium. The flow is governed by the Darcy law both in the fractures and in the porous matrix with large discontinuities in the permeability tensor. These fractures are supposed to have a small thickness with respect to the macroscopic length scale,
so that we can asymptotically reduce them to immersed polygonal fault
interfaces and the model finally consists in a coupling between a
2D elliptic problem and a 1D equation on the sharp interfaces modelling the fractures.
A cell-centered finite volume scheme on general polygonal meshes fitting the interfaces
is derived to solve the set of equations with the additional
differential transmission conditions linking both pressure and normal velocity
jumps through the interfaces.
We prove the convergence of the FV scheme for any set of data and parameters of the models and derive existence and uniqueness of the solution to the asymptotic models proposed.
The models are then numerically experimented for highly or partially immersed fractures.
Some numerical results are reported showing different kinds of flows
in the case of impermeable or partially/highly permeable fractures.
The influence of the variation of the aperture of the fractures is also investigated. The numerical
solutions of the asymptotic models are validated by comparing them to the solutions of the global Darcy model or to some analytic solutions.

LA - eng

KW - Fractured porous media; Darcy flow; finite volume method; asymptotic models of flow.; global solvability; cell-centered finite volume scheme; convergence; double-permeability model

UR - http://eudml.org/doc/250659

ER -

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## Citations in EuDML Documents

top- Luca Formaggia, Alessio Fumagalli, Anna Scotti, Paolo Ruffo, A reduced model for Darcy’s problem in networks of fractures
- Carlo D’Angelo, Anna Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids
- Peter Knabner, Jean E. Roberts, Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy–Forchheimer flow in the fracture
- Carlo D’Angelo, Anna Scotti, A mixed finite element method for Darcy flow in fractured porous media with non-matching grids

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