Journal ArticleDOI
Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body
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In this paper, the authors used matched asymptotic expansions to study the steady flow of a viscous incompressible fluid at low Reynolds number past a porous body of arbitrary shape.Abstract:
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 Holder 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.read more
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Dissertation
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References
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Boundary Integral Operators on Lipschitz Domains: Elementary Results
TL;DR: In this paper, the simple and double layer potentials for second order linear strongly elliptic differential operators on Lipschitz domains were studied and it was shown that in a certain range of Sobolev spaces, r...
Journal ArticleDOI
Expansions at small Reynolds numbers for the flow past a sphere and a circular cylinder
Ian Proudman,J. R. A. Pearson +1 more
TL;DR: In this paper, the Navier-Stokes equation is replaced by a set of differential equations for the coefficients ψn and Ψn, but only one set of physical boundary conditions is applicable to each expansion (the no-slip conditions for the Stokes expansion, and the uniform-stream condition for the Oseen expansion).
Journal ArticleDOI
Creeping flow relative to permeable spheres
TL;DR: In this paper, several possible solutions to the problem of creeping flow relative to an isolated permeable sphere are discussed and compared quantitatively, and the most satisfactory solutions are based upon Brinkman's extension of Darcy's Law.
Journal ArticleDOI
The Dirichlet problem for the Stokes system on Lipschitz domains
Journal ArticleDOI
Second kind integral equation formulation of Stokes' flows past a particle of arbitary shape
Henry Power,Guillermo Miranda +1 more
TL;DR: In this paper, the problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a single particle.
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