Importance sampling variance reduction for the Fokker-Planck rarefied gas particle method

JOURNAL OF COMPUTATIONAL PHYSICS

卷:325

Article

Collyer, B. S.^1,4  Connaughton, C.^1,2,4  Lockerby, D. A.³ 

[1] Univ Warwick, Ctr Complex Sci, Coventry CV4 7AL, W Midlands, England

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[3] Univ Warwick, Sch Engn, Coventry CV4 7AL, W Midlands, England

[4] London Math Lab, 14 Buckingham St, London WC2N 6DF, England

关键词: Rarefied gas flows;    Fokker-Planck equation;    Variance reduction;   

DOI  :  10.1016/j.jcp.2016.08.008

来源: Elsevier

【 摘 要 】

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. (C) 2016 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license.

【 授权许可】

Free