Homogenization of a dual-permeability problem in two-component media with imperfect contact

Abdelhamid Ainouz

Applications of Mathematics (2015)

  • Volume: 60, Issue: 2, page 185-196
  • ISSN: 0862-7940

Abstract

top
In this paper, we study the macroscopic modeling of a steady fluid flow in an ε -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.

How to cite

top

Ainouz, Abdelhamid. "Homogenization of a dual-permeability problem in two-component media with imperfect contact." Applications of Mathematics 60.2 (2015): 185-196. <http://eudml.org/doc/269890>.

@article{Ainouz2015,
abstract = {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.},
author = {Ainouz, Abdelhamid},
journal = {Applications of Mathematics},
keywords = {porous media; homogenization; two scale convergence; periodic homogenization; two-scale convergence; Darcy's law; flow in porous media},
language = {eng},
number = {2},
pages = {185-196},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Homogenization of a dual-permeability problem in two-component media with imperfect contact},
url = {http://eudml.org/doc/269890},
volume = {60},
year = {2015},
}

TY - JOUR
AU - Ainouz, Abdelhamid
TI - Homogenization of a dual-permeability problem in two-component media with imperfect contact
JO - Applications of Mathematics
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 185
EP - 196
AB - 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.
LA - eng
KW - porous media; homogenization; two scale convergence; periodic homogenization; two-scale convergence; Darcy's law; flow in porous media
UR - http://eudml.org/doc/269890
ER -

References

top
  1. Ainouz, A., Homogenized double porosity models for poro-elastic media with interfacial flow barrier, Math. Bohem. 136 (2011), 357-365. (2011) Zbl1249.35016MR2985545
  2. Ainouz, A., Homogenization of a double porosity model in deformable media, Electron. J. Differ. Equ. (electronic only) 2013 (2013), 1-18. (2013) Zbl1288.35038MR3065043
  3. Allaire, G., 10.1137/0523084, SIAM J. Math. Anal. 23 (1992), 1482-1518. (1992) Zbl0770.35005MR1185639DOI10.1137/0523084
  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. (1996) 
  5. T. Arbogast, J. Douglas, Jr., U. Hornung, 10.1137/0521046, SIAM J. Math. Anal. 21 (1990), 823-836. (1990) Zbl0698.76106MR1052874DOI10.1137/0521046
  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). (1978) Zbl0404.35001MR0503330
  7. Clark, G. W., 10.1006/jmaa.1998.6085, J. Math. Anal. Appl. 226 (1998), 364-376. (1998) Zbl0927.35081MR1650268DOI10.1006/jmaa.1998.6085
  8. Deresiewicz, H., Skalak, R., On uniqueness in dynamic poroelasticity, Bull. Seismol. Soc. Amer. 53 (1963), 783-788. (1963) 
  9. Ene, H. I., Poliševski, D., 10.1007/PL00013849, Z. Angew. Math. Phys. 53 (2002), 1052-1059. (2002) Zbl1017.35016MR1963553DOI10.1007/PL00013849
  10. Rohan, E., Naili, S., Cimrman, R., Lemaire, T., 10.1016/j.jmps.2012.01.013, J. Mech. Phys. Solids 60 (2012), 857-881. (2012) MR2899232DOI10.1016/j.jmps.2012.01.013
  11. Sanchez-Palencia, E., Non-Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127 Springer, Berlin (1980). (1980) Zbl0432.70002

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.