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Calculating effective diffusivities in the limit of vanishing molecular diffusion
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Pavliotis, G. A., Stuart, A. M. and Zygalakis, K. C.. (2009) Calculating effective diffusivities in the limit of vanishing molecular diffusion. Journal of Computational Physics, Vol.228 (No.4). pp. 1030-1055. ISSN 0021-9991
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Official URL: http://dx.doi.org/10.1016/j.jcp.2008.10.014
Abstract
In this paper we study the problem of the numerical calculation (by Monte Carlo methods) of the effective diffusivity for a particle moving in a periodic divergent-free velocity field, in the limit of vanishing molecular diffusion. In this limit traditional numerical methods typically fail, since they do not represent accurately the geometry of the underlying deterministic dynamics. We propose a stochastic splitting method that takes into account the volume-preserving property of the equations of motion in the absence of noise, and when inertial effects can be neglected. An extension of the method is then proposed for the cases where the noise has a non-trivial tune-correlation structure and when inertial effects cannot be neglected. The method of modified equations is used to explain failings of Euler-based methods. The new stochastic geometric integrators are shown to outperform standard Etder-based integrators. Various asymptotic limits of physical interest are investigated by means of numerical experiments, using the new integrators. (C) 2008 Elsevier Inc. All rights reserved.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software Q Science > QC Physics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | Journal of Computational Physics |
| Publisher: | Academic Press Inc. Elsevier Science |
| ISSN: | 0021-9991 |
| Date: | 1 March 2009 |
| Volume: | Vol.228 |
| Number: | No.4 |
| Number of Pages: | 26 |
| Page Range: | pp. 1030-1055 |
| Identification Number: | 10.1016/j.jcp.2008.10.014 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| Funder: | Warwick University through the Warwick Postgraduate Research Fellowship, Engineering and Physical Sciences Research Council (EPSRC) |
| URI: | http://wrap.warwick.ac.uk/id/eprint/28586 |
Data sourced from Thomson Reuters' Web of Knowledge
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