Periodic homogenization for inertial particles

PHYSICA D-NONLINEAR PHENOMENA

卷:204

Article

Pavliotis, GA ; Stuart, AM

关键词: inertial particles;    periodic homogenization;    effective diffusivity;    hypoellipticity;   

DOI  :  10.1016/j.physd.2005.04.011

来源: Elsevier

【 摘 要 】

We study the problem of homogenization for inertial particles moving in a periodic 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. To achieve this we use a formal multiple scale expansion in the scale parameter. This expansion relies on the hypo-ellipticity of the underlying diffusion. An expression for the diffusivity tensor is found and various of its properties studied. In particular, an expansion in terms of the non-dimensional particle relaxation time tau (the Stokes number) is shown to co-incide with the known result for passive (non-inertial) tracers in the singular limit tau -> 0. This requires the solution of a singular perturbation problem, achieved by means of a formal multiple scales expansion in tau Incompressible and potential fields are studied, as well as fields which are neither, and theoretical findings are supported by numerical simulations. (c) 2005 Elsevier B.V. All rights reserved.

【 授权许可】

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