Skip to main content
SpringerLink
Log in

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

  • Published:
Applications of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we study the macroscopic modeling of a steady fluid flow in an ɛ-periodic medium consisting of two interacting systems: fissures and blocks, with perme-abilities 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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Ainouz: Homogenized double porosity models for poro-elastic media with interfacial flow barrier. Math. Bohem. 136 (2011), 357–365.

    MATH  MathSciNet  Google Scholar 

  2. A. Ainouz: Homogenization of a double porosity model in deformable media. Electron. J. Differ. Equ. (electronic only) 2013 (2013), 1–18.

    Article  MathSciNet  Google Scholar 

  3. G. Allaire: Homogenization and two-scale convergence. SIAM J. Math. Anal. 23 (1992), 1482–1518.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. Allaire, A. Damlamian, U. Hornung: Two-scale convergence on periodic surfaces and applications. Proc. Int. Conference on Mathematical Modelling of Flow Through Porous Media, 1995 (A. Bourgeat et al., eds.). World Scientific Pub., Singapore, 1996, pp. 15–25.

    Google Scholar 

  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.

    Article  MATH  MathSciNet  Google Scholar 

  6. A. Bensoussan, J.-L. Lions, G. Papanicolaou: Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications 5, North-Holland Publ. Company, Amsterdam, 1978.

    MATH  Google Scholar 

  7. G. W. Clark: Derivation of microstructure models of fluid flow by homogenization. J. Math. Anal. Appl. 226 (1998), 364–376.

    Article  MATH  MathSciNet  Google Scholar 

  8. H. Deresiewicz, R. Skalak: On uniqueness in dynamic poroelasticity. Bull. Seismol. Soc. Amer. 53 (1963), 783–788.

    Google Scholar 

  9. H. I. Ene, D. Poliševski: Model of diffusion in partially fissured media. Z. Angew. Math. Phys. 53 (2002), 1052–1059.

    Article  MATH  MathSciNet  Google Scholar 

  10. E. Rohan, S. Naili, R. Cimrman, T. Lemaire: Multiscale modeling of a fluid saturated medium with double porosity: relevance to the compact bone. J. Mech. Phys. Solids 60 (2012), 857–881.

    Article  MathSciNet  Google Scholar 

  11. E. Sanchez-Palencia: Non-Homogeneous Media and Vibration Theory. Lecture Notes in Physics 127, Springer, Berlin, 1980.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory AMNEDP, Faculty of Mathematics, University of Sciences and Technology Houari Boumedienne, POB 32 El Alia, Algiers, Algeria

    Abdelhamid Ainouz

Authors
  1. Abdelhamid Ainouz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdelhamid Ainouz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ainouz, A. Homogenization of a dual-permeability problem in two-component media with imperfect contact. Appl Math 60, 185–196 (2015). https://doi.org/10.1007/s10492-015-0090-x

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10492-015-0090-x

Keywords

MSC 2010

Search

Navigation