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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

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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
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
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
Dates:
DateEvent
15 November 2016Published
15 September 2016Available
8 August 2016Accepted
4 December 2015Submitted
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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