Existence and uniqueness result for two-dimensional porous media flows with porous inclusions based on Brinkman equation

Kohr, Mirela; Sekhar, G. P. Raja

doi:10.1016/j.enganabound.2006.11.004

Cited by 11 publications

(10 citation statements)

References 23 publications

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“…Now, we require that the far field conditions (7) be satisfied by the outer expansions (18). Therefore, the termsf 0 (Re)v 0 andf 0 (Re)p 0 in the asymptotic expansions (18) should correspond to the uniform flow (i, 0), and hence we choosê…”

Section: Outer Expansionsmentioning

confidence: 99%

“…Therefore, the termsf 0 (Re)v 0 andf 0 (Re)p 0 in the asymptotic expansions (18) should correspond to the uniform flow (i, 0), and hence we choosê…”

Section: Outer Expansionsmentioning

confidence: 99%

“…In addition, by using the outer expansion (18), the relations (20) and (137), as well the expansions (97) of the Bessel functions K 0 and K 1 , we find for |x| →0 that…”

Section: The Complementary Single-layer Integral Operatormentioning

confidence: 99%

“…Re as Re → 0 withx fixed (25) In addition, let us make |x| →0 in the first of the outer expansions (18). Thus, in view of the relations (20), we have to consider the expansion…”

Section: The Matching For the Inner And Outer Expansionsmentioning

confidence: 99%

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Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body

Kohr

Wendland

Sekhar

2008

Math Methods in App Sciences

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SUMMARYIn 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.

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Section: Outer Expansionsmentioning

confidence: 99%

“…Therefore, the termsf 0 (Re)v 0 andf 0 (Re)p 0 in the asymptotic expansions (18) should correspond to the uniform flow (i, 0), and hence we choosê…”

Section: Outer Expansionsmentioning

confidence: 99%

“…In addition, by using the outer expansion (18), the relations (20) and (137), as well the expansions (97) of the Bessel functions K 0 and K 1 , we find for |x| →0 that…”

Section: The Complementary Single-layer Integral Operatormentioning

confidence: 99%

“…Re as Re → 0 withx fixed (25) In addition, let us make |x| →0 in the first of the outer expansions (18). Thus, in view of the relations (20), we have to consider the expansion…”

Section: The Matching For the Inner And Outer Expansionsmentioning

confidence: 99%

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Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body

Kohr

Wendland

Sekhar

2008

Math Methods in App Sciences

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“…Since the Brinkman equation is mathematically equivalent to the Stokes resolvent equation, the potential theory for the Stokes resolvent system may be used to treat several porous media flow problems which involve the Brinkman model. In view of this property, Kohr and Sekhar [20,21] have obtained existence and uniqueness for the problem of Stokes flow in a granular material with a void, or for the problem of two-dimensional porous media flows with porous inclusions based on Brinkman's equation, by assuming that the boundary of the flow domain is of class C 2,α , α ∈ (0, 1]. Also, Kohr, Sekhar, and Wendland [22] have used an indirect boundary integral method for the Stokes flow past a porous body, and have obtained some asymptotic results in both cases of large and, respectively, of low permeability of the porous body.…”

Section: Introductionmentioning

confidence: 96%

Boundary integral equations for a three‐dimensional Brinkman flow problem

Kohr

Wendland

2009

Mathematische Nachrichten

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The purpose of this paper is to prove existence and uniqueness in Sobolev or Hölder spaces for a transmission problem which describes the flow of a viscous incompressible fluid past a porous particle embedded in a second porous medium, by using the Brinkman model and potential theory. Some particular cases, which refer to Stokes flow past a porous particle, or to Brinkman's flow past a void, are also presented together with corresponding asymptotic results for the flow velocity field and the hydrodynamic force exerted on the particle.

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A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

Albişoru

2019

Mathematische Nachrichten

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The aim of this paper is to establish a well‐posedness result for a boundary value problem of transmission‐type for the standard and generalized Brinkman systems in two Lipschitz domains in R3, the former being bounded, and the latter, its complement in R3. As a first step, we establish a well‐posedness result for a transmission problem for the standard Brinkman systems on complementary Lipschitz domains in R3 by making use of the Potential theory developed for such a system. As a second step, we prove our desired result (in L2‐based Sobolev spaces) by using a method based on Fredholm operator theory and the well‐posedness result from the previous step.

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Existence and uniqueness result for two-dimensional porous media flows with porous inclusions based on Brinkman equation

Cited by 11 publications

References 23 publications

Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body

Boundary integral equations for two‐dimensional low Reynolds number flow past a porous body

Boundary integral equations for a three‐dimensional Brinkman flow problem

A layer potential analysis for transmission problems for Brinkman‐type systems in Lipschitz domains in

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