Advertisement

Journal of Evolution Equations

, Volume 16, Issue 1, pp 1–19 | Cite as

Mathematical analysis of variable density flows in porous media

  • Eduard Feireisl
  • Danielle Hilhorst
  • Hana Petzeltová
  • Peter Takáč
Article

Abstract

We consider a simple model describing the motion of a two-component mixture through a porous medium. We discuss well posedness of the associated initial-boundary value problem, in particular, with respect to the choice of boundary and far-field conditions. The existence of global-in-time solutions is proved in the ideal case when the fluid occupies the whole physical space. Finally, similar results are obtained also for the boundary value problems in the simplified 1-D geometry.

Keywords

Variable density flow Flows in porous media Global-in-time solutions 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ph. Clément, C. J. van Duijn, and Shuanhu Li. On a nonlinear elliptic-parabolic partial differential equation system in a two-dimensional groundwater flow problem. SIAM J. Math. Anal., 23(4):836–851, 1992.Google Scholar
  2. 2.
    Dentz M., Tartakovsky D.M., Abarca E., Guadagnini A., Sanchez-Vila X., Carrera J.: Variable-density flow in porous media. J. Fluid Mech., 561, 209–235 (2006)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Diersch H.-J.G., Kolditz O.: Variable-density flow and transport in porous media: approaches and challenges. Adv. Water Resources, 25, 899–944 (2002)CrossRefGoogle Scholar
  4. 4.
    van C.J. Duijn, L.A. Peletier, and R.-J. Schotting. Brine transport in porous media: self-similar solutions. Adv. Water Resources, 22:285–297, 1998.Google Scholar
  5. 5.
    Efendiev M. A., Fuhrmann J., Zelik S. V.: The long-time behaviour of the thermoconvective flow in a porous medium. Math. Methods Appl. Sci., 27(8), 907–930 (2004)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    D. Hilhorst, Huy Cuong Vu Do, and Y. Wang. A finite volume method for density driven flows in porous media. In CEMRACS’11: Multiscale coupling of complex models in scientific computing, volume 38 of ESAIM Proc., pages 376–386. EDP Sci., Les Ulis, 2012.Google Scholar
  7. 7.
    B. Johannsen. Numerische Aspekte dichtegetriebener Strömung in porösen Medien. Habilitation Thesis - https://sites.google.com/site/klausjohannsen/publications, 2004.
  8. 8.
    O. Kolditz, R. Ratke, H.-J.G. Diersch, and W. Zielke. Coupled groundwater flow and transport: 1. Verification of variable density flow and transport model. Adv. Water Resources, 21:27–46, 1998.Google Scholar

Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Eduard Feireisl
    • 1
  • Danielle Hilhorst
    • 2
  • Hana Petzeltová
    • 1
  • Peter Takáč
    • 3
  1. 1.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPrague 1Czech Republic
  2. 2.CNRS et Laboratoire de MathématiquesUniversité de Paris-SudOrsay CedexFrance
  3. 3.Institut für MathematikUniversität RostockRostockGermany

Personalised recommendations