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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.
Mots-clés : fractured porous media, Darcy flow, finite volume method, asymptotic models of flow
@article{M2AN_2009__43_2_239_0,
author = {Angot, Philippe and Boyer, Franck and Hubert, Florence},
title = {Asymptotic and numerical modelling of flows in fractured porous media},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {239--275},
publisher = {EDP-Sciences},
volume = {43},
number = {2},
year = {2009},
doi = {10.1051/m2an/2008052},
zbl = {1171.76055},
mrnumber = {2512496},
language = {en},
url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008052/}
}
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 PY - 2009 SP - 239 EP - 275 VL - 43 IS - 2 PB - EDP-Sciences UR - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008052/ DO - 10.1051/m2an/2008052 LA - en ID - M2AN_2009__43_2_239_0 ER -
%0 Journal Article %A Angot, Philippe %A Boyer, Franck %A Hubert, Florence %T Asymptotic and numerical modelling of flows in fractured porous media %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2009 %P 239-275 %V 43 %N 2 %I EDP-Sciences %U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008052/ %R 10.1051/m2an/2008052 %G en %F M2AN_2009__43_2_239_0
Angot, Philippe; Boyer, Franck; Hubert, Florence. Asymptotic and numerical modelling of flows in fractured porous media. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 2, pp. 239-275. doi : 10.1051/m2an/2008052. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2008052/
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