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

详细信息    查看全文

• 作者：B.S. Collyer^a ; ^d ; ^{benjamin.collyer@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; C. Connaughton^a ; ^b ; ^d ; D.A. Lockerby^c
• 关键词：Rarefied gas flows ; Fokker&ndash ; Planck equation ; Variance reduction
• 刊名：Journal of Computational Physics
• 出版年：2016
• 出版时间：15 November 2016
• 年：2016
• 卷：325
• 期：Complete
• 页码：116-128
• 全文大小：3152 K

文摘

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.