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The effect of roughness on the boundary condition on porous wall

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Abstract

The effects of roughness on the Darcy boundary condition for the Stokes system are studied using rigorous asymptotic analysis and homogenization techniques. Starting from the Stokes system in domain with porous part of the boundary and assuming that the porous boundary is periodically oscillating, we determine the effective permeability as a function of roughness.

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References

  1. Amirat, Y., Climent, B., Fernández-Cara, E., Simon, J.: The Stokes equations with Fourier boundary conditions on a wall with asperities. Math. Methods in the Appl. Sci. 24(5), 255–276 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amirat, Y., Climent, B., Fernández-Cara, E., Simon, J.: Effet de la rugosité sur un fluide laminaire avec conditions de Fourier. C.R.Acad.Sci.Paris, Série II b, t 328, 619-624 (2000)

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

    Article  Google Scholar 

  4. Belyaev, A.G., Chechkin, G.A., Gadyl’shin, R.R.: Effective membrane permeability: estimates and low concentration Asymptotics. SIAM J. Appl. Math. 60(1), 84–108 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. Carraro, T., Marušić-Paloka, E., Mikelić, A.: Effective pressure boundary condition for the filtration through porous medium via homogenization. Nonlinear Anal. Real World Appl. 44, 149–172 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  6. Casado-Diaz, J., Fernández-Cara, E., Simon, J.: Why viscous fluids adhere to rugose walls: a mathematical explanation. J. Diff. Equ. 189, 526–537 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  7. Chechkin, G., Friedman, A., Piatnitski, A.: The boundary-value problem in domains with very rapidly oscillating boundary. J. Math. Anal. Appl. 231, 213–234 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Galdi, G.P.: An introduction to the mathematical theory of the Navier-Stokes equations. Springer, Berlin (2011)

    Book  MATH  Google Scholar 

  9. Jäger, W., Mikelić, A.: Couette flows over a rough boundary and drag reduction. Commun. Math. Phys. 232, 429–455 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jäger, W., Mikelić, A.: On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60, 1111–1127 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  11. Marušić-Paloka, E.: Average of the Navier’s law on the rapidly oscillating boundary. J. Math. Anal. Appl. 259, 685–701 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Marušić-Paloka, E.: Effective fluid behavior in domain with rough boundary and the Darcy-Weisbach law. SIAM J. Appl. Math. 79, 1244–1270 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  13. Marušić-Paloka, E., Pažanin, I.: Effects of boundary roughness and inertia on the fluid flow through a corrugated pipe and the formula for the Darcy-Weisbach friction coefficient. Int. J. Eng. Sci. 152(103293), 1–13 (2020)

    MathSciNet  MATH  Google Scholar 

  14. Marušić-Paloka, E., Pažanin, I.: Rigorous justification of the effective boundary condition on a porous wall via homogenization. Z. Angew. Math. Phys. 72(146), 1–22 (2021)

    MathSciNet  MATH  Google Scholar 

  15. Marušić-Paloka, E., Pažanin, I.: The effective boundary condition on a porous wall. Int. J. Eng. Sci. 173(103638), 1–12 (2022)

    MathSciNet  MATH  Google Scholar 

  16. Marušić-Paloka, E., Starčević, M.: High-order approximations for an incompressible viscous flow on a rough boundary. Appl. Anal. 95, 1305–1333 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  17. Tio, K.-K., Sadhal, S.S.: Boundary conditions for Stokes flows near a porous membrane. Appl. Sci. Res. 52, 1–20 (1994)

    Article  MATH  Google Scholar 

  18. Sanchez-Palencia, E.: Non-homogeneous media and vibration theory. Springer, Berlin (1980)

    MATH  Google Scholar 

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Acknowledgements

The first author has been supported by the Croatian Science Foundation under the project AsAn (IP-2018-01-2735). The second author has been supported by the Croatian Science Foundation under the project MultiFM (IP-2019-04-1140).

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  1. Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Eduard Marušić-Paloka & Igor Pažanin

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  1. Eduard Marušić-Paloka
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  2. Igor Pažanin
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Correspondence to Eduard Marušić-Paloka.

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Marušić-Paloka, E., Pažanin, I. The effect of roughness on the boundary condition on porous wall. Z. Angew. Math. Phys. 74, 129 (2023). https://doi.org/10.1007/s00033-023-02016-7

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  • DOI: https://doi.org/10.1007/s00033-023-02016-7

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