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Date
2022Type
- Journal Article
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Abstract
This article is a sequel to our previous work [SIAM J. Math. Anal., 53 (2021), pp. 2890--2924] concerned with the derivation of high order homogenized models for the Stokes equation in a periodic porous medium. We provide an improved asymptotic analysis of the coefficients of the higher order models in the low-volume fraction regime whereby the periodic obstacles are rescaled by a factor η which converges to zero. By introducing a new family of order k corrector tensors with a controlled growth as η→0 uniform in k∈N, we are able to show that both the infinite order and the finite order models converge in a coefficient-wise sense to the three classical asymptotic regimes. Namely, we retrieve the Darcy model, the Brinkman equation or the Stokes equation in the homogeneous cubic domain depending on whether η is respectively larger, proportional to, or smaller than the critical size ηcrit∼ϵ2/(d−2). For completeness, the paper first establishes the analogous results for the perforated Poisson equation, considered as a simplified scalar version of the Stokes system. Show more
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publishedExternal links
Journal / series
SIAM Journal on Mathematical AnalysisVolume
Pages / Article No.
Publisher
SIAMSubject
Homogenization; Higher order models; Perforated Poisson problem; Stokcs system; Low-volume fraction asymptotics; Strange termOrganisational unit
09504 - Ammari, Habib / Ammari, Habib
02500 - Forschungsinstitut für Mathematik / Institute for Mathematical Research
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Is new version of: http://hdl.handle.net/20.500.11850/491113
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