| Issue |
ESAIM: M2AN
Volume 55, Number 3, May-June 2021
|
|
|---|---|---|
| Page(s) | 789 - 805 | |
| DOI | https://doi.org/10.1051/m2an/2020087 | |
| Published online | 05 May 2021 | |
Thermal flows in fractured porous media
1
Univ Rennes, UR1, CNRS, IRMAR – UMR 6625, F-35000 Rennes, France
2
I.M.A.R., P.O. Box 1-764, Bucharest, Romania
* Corresponding author: isabelle.gruais@univ-rennes1.fr
Received:
23
April
2020
Accepted:
14
December
2020
We consider the thermal flow problem occuring in a fractured porous medium. The incompressible filtration flow in the porous matrix and the viscous flow in the fractures obey the Boussinesq approximation of Darcy-Forchheimer law and respectively, the Stokes system. They are coupled by the Saffman’s variant of the Beavers–Joseph condition. Existence and uniqueness properties are presented. The use of the energy norm in describing the Darcy-Forchheimer law proves to be appropriate. In the ε-periodic framework, we find the two-scale homogenized system which governs their asymptotic behaviours when ε → 0 and the Forchheimer effect vanishes. The limit problem is mainly a model of two coupled thermal flows, neither of them being incompressible.
Mathematics Subject Classification: 35B27 / 76M50 / 76Rxx / 74F10 / 74Q05
Key words: Fractured porous media / ε-domes / two-scale homogenized system / Darcy-Forchheimer law / Boussinesq approximation / Beavers–Joseph condition
© EDP Sciences, SMAI 2021
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