Homogenization for inertial particles in a random flow
Abstract
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.
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.Attached Files
Submitted - 0702022.pdf
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Additional details
- Eprint ID
- 71847
- Resolver ID
- CaltechAUTHORS:20161108-174342361
- Warwick University
- Engineering and Physical Sciences Research Council (EPSRC)
- Created
-
2016-11-10Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field
- Other Numbering System Name
- Andrew Stuart
- Other Numbering System Identifier
- J71