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

Journal Article · Tue Nov 15 04:00:00 EST 2016 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2016.08.008· OSTI ID:22622209

Connaughton, C. ^[1]; Lockerby, D. A. ^[2]

---

1. Centre for Complexity Science, University of Warwick, Coventry CV4 7AL (United Kingdom)
2. School of Engineering, University of Warwick, Coventry, CV4 7AL (United Kingdom)

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.

• OSTI ID: 22622209
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 325; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
BOLTZMANN EQUATION
COMPARATIVE EVALUATIONS
COUETTE FLOW
FOKKER-PLANCK EQUATION
GAS FLOW
NOISE
REDUCTION
RELAXATION
SAMPLING
STOCHASTIC PROCESSES
VELOCITY