Viscous boundary layers in flows through a domain with permeable boundary

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The effect of small viscosity on nearly inviscid flows of an incompressible fluid through a given domain with permeable boundary is studied. The Vishik-Lyustemik method is applied to construct a boundary layer asymptotic at the outlet in the limit of vanishing viscosity. Mathematical problems with both consistent and inconsistent initial and boundary conditions at the outlet are considered. It is shown that in the former case, the viscosity leads to a boundary layer only at the outlet. In the latter case, in the leading term of the expansion there is a boundary layer at the outlet and there is no boundary layer at the inlet, but in higher order terms another boundary layer appears at the inlet. To verify the validity of the expansion, a number of simple examples are presented. The examples demonstrate that asymptotic solutions are in quite good agreement with exact or numerical solutions. (C) 2007 Elsevier Masson SAS. All rights reserved.

Original languageEnglish
Pages (from-to)514-538
Number of pages25
JournalEuropean journal of mechanics b-Fluids
Issue number5
Publication statusPublished - Sept 2008


  • Fluid Dynamics
  • Boundary layer;
  • Permeable boundary;
  • Vanishing viscosity

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