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Importance sampling variance reduction for the Fokker-Planck rarefied gas particle method
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Collyer, Benjamin S., Connaughton, Colm and Lockerby, Duncan A. (2016) Importance sampling variance reduction for the Fokker-Planck rarefied gas particle method. Journal of Computational Physics, 325 . pp. 116-128.
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Official URL: http://dx.doi.org/10.1016/j.jcp.2016.08.008
Abstract
The Fokker–Planck approximation to the Boltzmann equation, solved numerically by stochastic particle schemes, is used to provide estimates for rarefied gas flows. This paper presents a variance reduction technique for a stochastic particle method that is able to greatly reduce the uncertainty of the estimated flow fields when the characteristic speed of the flow is small in comparison to the thermal velocity of the gas. The method relies on importance sampling, requiring minimal changes to the basic stochastic particle scheme. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find that our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed.
| Item Type: | Journal Article | ||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science > Mathematics | ||||||||||
| Library of Congress Subject Headings (LCSH): | Fokker-Planck equation, Navier-Stokes equations, Transport theory | ||||||||||
| Journal or Publication Title: | Journal of Computational Physics | ||||||||||
| Publisher: | Academic Press Inc. Elsevier Science | ||||||||||
| ISSN: | 0021-9991 | ||||||||||
| Official Date: | 15 November 2016 | ||||||||||
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| Volume: | 325 | ||||||||||
| Page Range: | pp. 116-128 | ||||||||||
| Status: | Peer Reviewed | ||||||||||
| Publication Status: | Published | ||||||||||
| Access rights to Published version: | Open Access | ||||||||||
| Funder: | Engineering and Physical Sciences Research Council (EPSRC) | ||||||||||
| Grant number: | EP/I011927/1 and EP/N016602/1 |
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