| Title:
|
Homogenization of a dual-permeability problem in two-component media with imperfect contact (English) |
| Author:
|
Ainouz, Abdelhamid |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
60 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
185-196 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we study the macroscopic modeling of a steady fluid flow in an $\varepsilon $-periodic medium consisting of two interacting systems: fissures and blocks, with permeabilities of different order of magnitude and with the presence of flow barrier formulation at the interfacial contact. The homogenization procedure is performed by means of the two-scale convergence technique and it is shown that the macroscopic model is a one-pressure field model in a one-phase flow homogenized medium. (English) |
| Keyword:
|
porous media |
| Keyword:
|
homogenization |
| Keyword:
|
two scale convergence |
| MSC:
|
35B27 |
| MSC:
|
76S05 |
| idZBL:
|
Zbl 06433678 |
| idMR:
|
MR3320344 |
| DOI:
|
10.1007/s10492-015-0090-x |
| . |
| Date available:
|
2015-03-09T17:31:54Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144170 |
| . |
| Reference:
|
[1] Ainouz, A.: Homogenized double porosity models for poro-elastic media with interfacial flow barrier.Math. Bohem. 136 (2011), 357-365. Zbl 1249.35016, MR 2985545 |
| Reference:
|
[2] Ainouz, A.: Homogenization of a double porosity model in deformable media.Electron. J. Differ. Equ. (electronic only) 2013 (2013), 1-18. Zbl 1288.35038, MR 3065043 |
| Reference:
|
[3] Allaire, G.: Homogenization and two-scale convergence.SIAM J. Math. Anal. 23 (1992), 1482-1518. Zbl 0770.35005, MR 1185639, 10.1137/0523084 |
| Reference:
|
[4] Allaire, G., Damlamian, A., Hornung, U.: Two-scale convergence on periodic surfaces and applications.Proc. Int. Conference on Mathematical Modelling of Flow Through Porous Media, 1995 A. Bourgeat et al. World Scientific Pub., Singapore (1996), 15-25. |
| Reference:
|
[5] T. Arbogast, J. Douglas, Jr., U. Hornung: Derivation of the double porosity model of single phase flow via homogenization theory.SIAM J. Math. Anal. 21 (1990), 823-836. Zbl 0698.76106, MR 1052874, 10.1137/0521046 |
| Reference:
|
[6] Bensoussan, A., Lions, J.-L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures.Studies in Mathematics and its Applications 5 North-Holland Publ. Company, Amsterdam (1978). Zbl 0404.35001, MR 0503330 |
| Reference:
|
[7] Clark, G. W.: Derivation of microstructure models of fluid flow by homogenization.J. Math. Anal. Appl. 226 (1998), 364-376. Zbl 0927.35081, MR 1650268, 10.1006/jmaa.1998.6085 |
| Reference:
|
[8] Deresiewicz, H., Skalak, R.: On uniqueness in dynamic poroelasticity.Bull. Seismol. Soc. Amer. 53 (1963), 783-788. |
| Reference:
|
[9] Ene, H. I., Poliševski, D.: Model of diffusion in partially fissured media.Z. Angew. Math. Phys. 53 (2002), 1052-1059. Zbl 1017.35016, MR 1963553, 10.1007/PL00013849 |
| Reference:
|
[10] Rohan, E., Naili, S., Cimrman, R., Lemaire, T.: Multiscale modeling of a fluid saturated medium with double porosity: relevance to the compact bone.J. Mech. Phys. Solids 60 (2012), 857-881. MR 2899232, 10.1016/j.jmps.2012.01.013 |
| Reference:
|
[11] Sanchez-Palencia, E.: Non-Homogeneous Media and Vibration Theory.Lecture Notes in Physics 127 Springer, Berlin (1980). Zbl 0432.70002 |
| . |
