Sharp convergence rates for Darcy's law

This article is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp convergence rate in a periodically perforated and bounded domain in for where ε represents the size of solid obstacles. This is achieved by constructing two boundary...

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Bibliographic Details
Published inCommunications in partial differential equations Vol. 47; no. 6; pp. 1098 - 1123
Main Author Shen, Zhongwei
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.06.2022
Taylor & Francis Ltd
Subjects
Asymptotic series
Boundary layers
Convergence
convergence rate
Darcy's Law
Fluid flow
Incompressibility
Incompressible flow
Porous media
stokes equations
Viscous fluids
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ISSN0360-5302
1532-4133
DOI10.1080/03605302.2022.2037634

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Summary:This article is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp convergence rate in a periodically perforated and bounded domain in for where ε represents the size of solid obstacles. This is achieved by constructing two boundary layer correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.
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ISSN:0360-5302
1532-4133
DOI:10.1080/03605302.2022.2037634