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)
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.
|Subjects:||D - G > General|
|Research Groups:||Oxford Centre for Collaborative Applied Mathematics|
|Deposited By:||Kate Lewin|
|Deposited On:||11 Feb 2010 08:05|
|Last Modified:||11 Feb 2010 08:05|
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