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Homogenization for inertial particles in a random flow

Pavliotis, G. A. and Stuart, A. M. and Zygalakis, K. C. (2007) Homogenization for inertial particles in a random flow. Communications in Mathematical Sciences, 5 (3). pp. 507-531. ISSN 1539-6746. doi:10.4310/CMS.2007.v5.n3.a1.

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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.

Item Type:Article
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Additional Information:© 2007 International Press. Received: February 8, 2007; accepted (in revised version): April 19, 2007. Communicated by Weinan E. The authors thank the Center for Scientific Computing at Warwick University for computational resources. K.Z. was supported by Warwick University through Warwick Postgraduate Research Fellowship (WP RF) and by EPSRC.
Funding AgencyGrant Number
Warwick UniversityUNSPECIFIED
Engineering and Physical Sciences Research Council (EPSRC)UNSPECIFIED
Subject Keywords:homogenization theory, multiscale analysis, martingale central limit theorem, hypoelliptic diffusions, Gaussian velocity fields
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Other Numbering System NameOther Numbering System ID
Andrew StuartJ71
Issue or Number:3
Classification Code:AMS subject classifications. 60H10, 60H15, 60H30, 60G15
Record Number:CaltechAUTHORS:20161108-174342361
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71847
Deposited By: Linda Taddeo
Deposited On:10 Nov 2016 00:08
Last Modified:11 Nov 2021 04:52

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