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Contributions to Partial Differential Equations and Applications pp 395–410Cite as

On Some Weighted Stokes Problems: Applications on Smagorinsky Models

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Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 47))

Abstract

In this paper we study existence and uniqueness of weak solutions for some non-linear weighted Stokes problems using convex analysis. The characterization of these equations is the viscosity, which depends on the strain rate of the velocity field and in some cases is related with a weight being the distance to the boundary of the domain. Such non-linear relations can be seen as a first approach of mixing-length eddy viscosity from turbulent modeling. A well known model is von Karman’s on which the viscosity depends on the square of the distance to the boundary of the domain. Numerical experiments conclude the work and show properties from the theory.

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Acknowledgements

The authors would like to thank Rio-Tinto Alcan Company for their financial support and Agnieska Kalamaskya for her input on Korn’s Inequalities.

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Authors and Affiliations

  1. Ecole Polytechnique Fédérale de Lausanne, 1015, Lausanne, Switzerland

    Jacques Rappaz & Jonathan Rochat

Authors
  1. Jacques Rappaz
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  2. Jonathan Rochat
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Correspondence to Jacques Rappaz .

Editor information

Editors and Affiliations

  1. Keldysh Institute of Applied Mathematics (IPM), Moscow, Russia

    B. N. Chetverushkin

  2. College of Technology, University of Houston, Houston, TX, USA

    W. Fitzgibbon

  3. Department of Mathematics, University of Houston, Houston, TX, USA

    Y.A. Kuznetsov

  4. Department of Mathematical Information, University of Jyväskylä, Jyväskylä, Finland

    P. Neittaanmäki

  5. University of Jyväskylä, Jyväskylä, Finland

    J. Periaux

  6. LJLL-UPMC, Paris, France

    O. Pironneau

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Rappaz, J., Rochat, J. (2019). On Some Weighted Stokes Problems: Applications on Smagorinsky Models. In: Chetverushkin, B., Fitzgibbon, W., Kuznetsov, Y., Neittaanmäki, P., Periaux, J., Pironneau, O. (eds) Contributions to Partial Differential Equations and Applications. Computational Methods in Applied Sciences, vol 47. Springer, Cham. https://doi.org/10.1007/978-3-319-78325-3_21

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  • DOI: https://doi.org/10.1007/978-3-319-78325-3_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-78324-6

  • Online ISBN: 978-3-319-78325-3

  • eBook Packages: EngineeringEngineering (R0)

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