Viscous boundary layers in flows through a domain with permeable boundary

TY - JOUR

T1 - Viscous boundary layers in flows through a domain with permeable boundary

AU - Ilin, K.

PY - 2008/9

Y1 - 2008/9

N2 - 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.

AB - 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.

KW - Fluid Dynamics

KW - Boundary layer;

KW - Permeable boundary;

KW - Vanishing viscosity

UR - http://www.scopus.com/inward/record.url?scp=47549096449&partnerID=8YFLogxK

U2 - 10.1016/j.euromechflu.2007.10.003

DO - 10.1016/j.euromechflu.2007.10.003

M3 - Article

SN - 0997-7546

VL - 27

SP - 514

EP - 538

JO - European journal of mechanics b-Fluids

JF - European journal of mechanics b-Fluids

IS - 5

ER -