High order homogenized Stokes models capture all three regimes
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2021-01
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Report
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Abstract
This article is a sequel to our previous work 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.
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published
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2021-02
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Seminar for Applied Mathematics, ETH Zurich
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Homogenization; Higher order models; Perforated poisson problem; Stokes system; Low volume fraction asymptotics; Strange term
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09504 - Ammari, Habib / Ammari, Habib
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