Skip to main content

Interface Conditions for Arbitrary Flows in Coupled Porous-Medium and Free-Flow Systems

  • Conference paper
  • First Online:
Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples (FVCA 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 323))

Included in the following conference series:

  • 1167 Accesses

Abstract

Physically consistent interface conditions are important for accurate mathematical modelling and numerical simulation of flow and transport processes in coupled free-flow and porous-medium systems. Traditional coupling concepts are valid for simplified cases only, such as flows parallel to the fluid-porous interface or very specific boundary value problems. This severely limits the range of applications that can be accurately modelled. Evidently, there is a need for more general interface conditions to couple free flow to porous-medium flow. In this paper, we propose new coupling conditions for arbitrary flow directions and periodic porous media. These conditions are derived by the theory of homogenisation and boundary layers and are applicable to general filtration problems. The derived set of coupling conditions are validated by comparison of pore-scale to macroscale numerical simulations.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Angot, P., Goyeau, B., Ochoa-Tapia, J.A.: Asymptotic modeling of transport phenomena at the interface between a fluid and a porous layer: jump conditions. Phys. Rev. E 95, 063302 (2017)

    Article  MathSciNet  Google Scholar 

  2. Beavers, G.S., Joseph, D.D.: Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207 (1967)

    Article  Google Scholar 

  3. Carraro, T., Goll, C., Marciniak-Czochra, A., Mikelić, A.: Effective interface conditions for the forced infiltration of a viscous fluid into a porous medium using homogenization. Comput. Methods Appl. Mech. Engrg. 292, 195–220 (2015)

    Article  MathSciNet  Google Scholar 

  4. Discacciati, M., Gerardo-Giorda, L.: Optimized Schwarz methods for the Stokes–Darcy coupling. IMA J. Numer. Anal. 38, 1959–1983 (2018)

    Article  MathSciNet  Google Scholar 

  5. Discacciati, M., Quarteroni, A.: Navier–Stokes/Darcy coupling: modeling, analysis, and numerical approximation. Rev. Mat. Complut. 22, 315–426 (2009)

    Article  MathSciNet  Google Scholar 

  6. Eggenweiler, E., Rybak, I.: Unsuitability of the Beavers–Joseph interface condition for filtration problems. J. Fluid Mech. (2020). https://doi.org/10.1017/jfm.2020.194

  7. Hecht, F.: New development in FreeFem++. J. Numer. Math. 20, 251–265 (2012)

    Article  MathSciNet  Google Scholar 

  8. Hornung, U.: Homogenization and Porous Media. Springer, Berlin (1997)

    Google Scholar 

  9. Jäger, W., Mikelić, A.: On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 23, 403–465 (1996)

    Google Scholar 

  10. Jäger, W., Mikelić, A.: Modeling effective interface laws for transport phenomena between an unconfined fluid and a porous medium using homogenization. Transp. Porous Media 78, 489–508 (2009)

    Article  MathSciNet  Google Scholar 

  11. Lācis, U., Bagheri, S.: A framework for computing effective boundary conditions at the interface between free fluid and a porous medium. J. Fluid Mech. 812, 866–889 (2017)

    Article  MathSciNet  Google Scholar 

  12. Rybak, I., Schwarzmeier, C., Eggenweiler, E., Rüde, U.: Validation and calibration of coupled porous-medium and free-flow problems using pore-scale resolved models. Comput. Geosci. (submitted) (arXiv:1906.06884v2) (2019)

  13. Saffman, P.G.: On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50, 93–101 (1971)

    Article  Google Scholar 

  14. Versteeg, H., Malalasekra, W.: An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Prentice Hall (2007)

    Google Scholar 

Download references

Acknowledgements

The work is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 327154368—SFB 1313.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Elissa Eggenweiler .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Eggenweiler, E., Rybak, I. (2020). Interface Conditions for Arbitrary Flows in Coupled Porous-Medium and Free-Flow Systems. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_31

Download citation

Publish with us

Policies and ethics