The Mathematical Institute, University of Oxford, Eprints Archive

Homogenization for advection-diffusion in a perforated domain

Haynes, P.H. and Hoang, V.H. and Norris, J.R. and Zygalakis, K. C. (2010) Homogenization for advection-diffusion in a perforated domain. Not specified . (Submitted)

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Abstract

The volume of a Wiener sausage constructed from a diffusion process with periodic, mean-zero, divergence-free velocity field, in dimension 3 or more, is shown to have a non-random and positive asymptotic rate of growth. This is used to establish the existence of a homogenized limit for such a diffusion when subject to Dirichlet conditions on the boundaries of a sparse and independent array of obstacles. There is a constant effective long-time loss rate at the obstacles. The dependence of this rate on the form and intensity of the obstacles and on the velocity field is investigated. A Monte Carlo algorithm for the computation of the volume growth rate of the sausage is introduced and some numerical results are presented for the Taylor–Green velocity field.

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:895
Deposited By:Kate Lewin
Deposited On:11 Feb 2010 08:05
Last Modified:11 Feb 2010 08:05

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