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Applicable Analysis
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Volume 94, 2015 - Issue 7
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Articles

High-order approximations for an incompressible viscous flow on a rough boundary

Eduard Marušić-PalokaFaculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, 1000, Croatia.
&
Maja StarčevićFaculty of Science, Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, 1000, Croatia.Correspondence[email protected]
Pages 1305-1333 | Received 03 Feb 2014, Accepted 01 Jun 2014, Published online: 01 Jul 2014

References

  • Achdou Y, Pironneau O, Valentin F. Shape control versus boundary control. In: Equations aux dérivées partielles et applications. Articles dédiés à Lions JL. Paris: Elsevier; 1998. p. 1–18.
  • Achdou Y, Pironneau O, Valentin F. Effective boundary conditions for laminar flows over periodic rough boundaries. J. Comput. Phys. 1998;147:187–218.
  • Mohammadi B, Pironneau O, Valentin F. Rough boundaries and wall laws. Int. J. Numer. Meth. Fluids. 1998;27:169–177.
  • Amirat Y, Simon J. Influence de la rugosité en hydrodynamique laminaire. C. R. Acad. Sci. Paris, Série I. 1996;323:313–318.
  • Amirat Y, Simon J. Riblet and drag minimization. In: Cox S, Lasiecka I, editor. Optimization methods in PDEs. Vol. 209, Contemporary mathematics. Providence (RI): American Mathematical Society; 1997. p. 9–18.
  • Jäger W, Mikelić A. On the roughness-induced effective boundary conditions for an incompressible viscous flow. J. Differ. Equ. 2001;170:96–122.
  • Jäger W, Mikelić A. Couette flows over a rough boundary and drag reduction. Comm. Math. Phys. 2003;232:429–455.
  • Gérard-Varet D. The Navier wall law at a boundary with random roughness. Comm. Math. Phys. 2009;286:81–110.
  • Gérard-Varet D, Masmoudi N. Relevance of the slip condition for fluid flows near an irregular boundary. Comm. Math. Phys. 2010;295:99–137.
  • Madureira AL, Valentin F. Asymptotics of the Poisson problem in domains with curved rough boundaries. SIAM J. Math. Anal. 2007;38:1450–1473.
  • Neuss N, Neuss-Radu M, Mikelić A. Effective laws for the Poisson equation on domains with curved oscillating boundaries. Appl. Anal. 2006;85:479–502.
  • Amirat Y, Bodart O, De Maio U, Gaudiello A. Effective boundary condition for Stokes flow over a very rough surface. J. Differ. Equ. 2013;254:3395–3430.
  • Bresch D, Milisic V. High order multi-scale wall-laws, Part I: the periodic case. Quart. Appl. Math. 2010;68:229–253.
  • Bresch D, Milisic V. Towards implicit multi-scale wall laws. C. R. Math. Acad. Sci. Paris. 2008;346:833–838.
  • Jäger W, Mikelić A. On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Sc. Norm. Sup. Pisa Cl. Sci. Fis. Mat. 1996;23:403–465.
  • Galdi GP. An Introduction to the mathematical theory of the Navier–Stokes equations. New York, NY: Springer-Verlag; 2011.

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