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Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body
Author(s) -
Kohr Mirela,
Wendland Wolfgang L.,
Raja Sekhar G. P.
Publication year - 2008
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1074
Subject(s) - mathematics , reynolds number , mathematical analysis , porous medium , integral equation , sobolev space , body force , flow (mathematics) , asymptotic expansion , geometry , mechanics , porosity , physics , materials science , turbulence , composite material
In this paper we use the method of matched asymptotic expansions in order to study the two‐dimensional steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape. One assumes that the flow inside the porous body is described by the Brinkman model, i.e. by the continuity and Brinkman equations, and that the velocity and boundary traction fields are continuous across the interface between the fluid and porous media. By considering some indirect boundary integral representations, the inner problems are reduced to uniquely solvable systems of Fredholm integral equations of the second kind in some Sobolev or Hölder spaces, while the outer problems are solved by using the singularity method. It is shown that the force exerted by the exterior flow on the porous body admits an asymptotic expansion with respect to low Reynolds number, whose terms depend on the solutions of the abovementioned system of boundary integral equations. In addition, the case of small permeability of the porous body is also treated. Copyright © 2008 John Wiley & Sons, Ltd.