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Article Dans Une Revue Asymptotic Analysis Année : 2022

A simple justification of effective models for conducting or fluid media with dilute spherical inclusions

Résumé

We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of n ≫ 1 spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as n → + ∞ by simple arguments.

Dates et versions

hal-04528388 , version 1 (01-04-2024)

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David Gérard-Varet. A simple justification of effective models for conducting or fluid media with dilute spherical inclusions. Asymptotic Analysis, 2022, 128 (1), pp.31-53. ⟨10.3233/asy-211696⟩. ⟨hal-04528388⟩
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