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Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture

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Multiscale Problems in Science and Technology

Abstract

We study the fluid flow through a thin fracture with prescribed pressure drop. We suppose that the fracture has a constriction such that the flow is not purely Poiseuille. We find the corrector for the Poiseuille flow due to the constriction, we prove the corresponding error estimate and we illustrate the theoretical results by some numerical experiments.

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References

  1. Blanc F., Gipouloux O., Panasenko G., Zine A.M. (1999) Asymptotic analysis and partial asymptotic decomposition of domain for Stokes Equation in tube structure. Math. Models Methods Appl. Sei. M3 AS 9(9), 1351–1378

    Article  MathSciNet  MATH  Google Scholar 

  2. Bourgeat A., Marusic-Paloka E. (1998) Nonlinear Effects for Flow in Periodically Constricted Channel Caused by High Injection Rate. Math. Models Methods Appl. Sei. M3 AS 9(8), 1–25

    Google Scholar 

  3. Conca C, Murat F., Pironneau O. (1994) The Stokes and Navier-Stokes equations with boundary conditions involving the pressure. Japan J. Math. 20, 263–318

    MathSciNet  Google Scholar 

  4. Duvnjak A., Marušić-Paloka E. (2000) Derivation of the Reynolds equation for lubrication of a rotating shaft. Arch. Math. (Brno) 36(4), 239–253

    MathSciNet  MATH  Google Scholar 

  5. Heywood J.G., Rannacher R., Turek S. (1996) Artificial boundaries and flux and pressure conditions for the incompressible Navier-Stokes equations. Int. J. Numer. Methods Fluids 22, 325–352

    Article  MathSciNet  MATH  Google Scholar 

  6. Marušić-Paloka E. (2001) Fluid flow through a network of thin pipes. C. R. Acad. Sei. Paris, Série II b 329

    Google Scholar 

  7. Nazarov S.A., Piletskas K.I. (1991) The Reynolds Flow in a Thin Three-Dimensional Channel, Lithuanian Math. J. 30, 366–375

    Article  MathSciNet  Google Scholar 

  8. Panasenko G. (1998) Asymptotic expansion of the solution of Navier-Stokes equation in a tube structure. C. R. Acad. Sei. Paris, Série II b, 326, 867–872

    MathSciNet  MATH  Google Scholar 

  9. Brezzi, F. (1974) On the existence, uniqueness and approximation of saddle points arising from Lagrangian multipliers. R.A.I.R.O., ser. Num. Anal. 8

    Google Scholar 

  10. Brezzi, F., Fortin, M. (1991) Mixed and Hybrid Finite Element Methods. Springer

    Google Scholar 

  11. Fortin, M., Fortin, A. (1985) Experiments with several elements for viscous incompressible flows. Int. J. numer. methods fluids 5, 911–928

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Calcul Scientifique et Modélisation Mathématique, Université de Saint Etienne, 23 Rue du Docteur P. Michelon, 42023, Saint Etienne, France

    Olivier Gipouloux

  2. Laboratoire de Mécanique et d’Acoustique, 31 Chemin Joseph Aiguier 13402, Marseille, France

    Olivier Gipouloux

  3. Department of Mathematics, University of Zagreb, Bijenička 30, 10000, Zagreb, Croatia

    Eduard Marušić-Paloka

Authors
  1. Olivier Gipouloux
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  2. Eduard Marušić-Paloka
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Editor information

Editors and Affiliations

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

    Nenad Antonić

  2. Dept. of Applied Analysis and Scientific Computing, CWI Amsterdam, P.O.Box 94079, Kruislaan 413, 1090 GB, Amsterdam, The Netherlands

    C. J. van Duijn

  3. IWR, University of Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Willi Jäger

  4. Analyse Numérique, Bât 101 U.F.R. Mathématiques, Université Lyon 1, 43, Bd. du 11 Novembre 1918, 69622, Villeurbanne Cedex, France

    Andro Mikelić

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© 2002 Springer-Verlag Berlin Heidelberg

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Gipouloux, O., Marušić-Paloka, E. (2002). Asymptotic Behaviour of the Incompressible Newtonian Flow Through Thin Constricted Fracture. In: Antonić, N., van Duijn, C.J., Jäger, W., Mikelić, A. (eds) Multiscale Problems in Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56200-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-56200-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43584-6

  • Online ISBN: 978-3-642-56200-6

  • eBook Packages: Springer Book Archive

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