Open Access
September 2007 Homogenization for inertial particles in a random flow
G.A. Pavliotis, A.M. Stuart, K.C> Zygalakis
Commun. Math. Sci. 5(3): 507-531 (September 2007).


We study the problem of homogenization for inertial particles moving in a time-dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large-scale, long-time behavior of the inertial particles is governed by an effective diffusion equation for the position variable alone. This is achieved by the use of a formal multiple scales expansion in the scale parameter. The expansion relies on the hypoellipticity of the underlying diffusion. An expression for the diffusivity tensor is found and various of its properties are studied. The results of the formal multiscale analysis are justified rigorously by the use of the martingale central limit theorem. Our theoretical findings are supported by numerical investigations where we study the parametric dependence of the effective diffusivity on the various non-dimensional parameters of the problem.


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G.A. Pavliotis. A.M. Stuart. K.C> Zygalakis. "Homogenization for inertial particles in a random flow." Commun. Math. Sci. 5 (3) 507 - 531, September 2007.


Published: September 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1133.60338
MathSciNet: MR2352329

Primary: 60G15 , 60H10 , 60H15 , 60H30

Keywords: Gaussian velocity fields , homogenization theory , Hypoelliptic diffusions , martingale central limit theorem , multiscale analysis

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 3 • September 2007
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