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arXiv · 1003.3990

Homogenization for advection-diffusion in a perforated domain

P. H. Haynes·V. H. Hoang·J. R. Norris·K. C. Zygalakis
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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.

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P. H. Haynes, V. H. Hoang, J. R. Norris, K. C. Zygalakis. 2010-03-25. Homogenization for advection-diffusion in a perforated domain. https://arxiv.org/abs/1003.3990

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