Variance reduction for Monte Carlo solutions of the Boltzmann equation

被引:125
作者
Baker, LL [1 ]
Hadjiconstantinou, NG [1 ]
机构
[1] MIT, Dept Mech Engn, Cambridge, MA 02139 USA
关键词
D O I
10.1063/1.1899210
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
We show that by considering only the deviation from equilibrium, significant computational savings can be obtained in Monte Carlo evaluations of the Boltzmann collision integral for flow problems in the small Mach number (Ma) limit. The benefits of this variance reduction approach include a significantly reduced statistical uncertainty when the deviation from equilibrium is small, and a flow-velocity signal-to-noise ratio that remains approximately constant with Ma in the Ma < 1 limit. This results in stochastic Boltzmann solution methods whose computational cost for a given signal-to-noise ratio is essentially independent of Ma for Ma < 1; our numerical implementation demonstrates this for Mach numbers as low as 10(-5). These features are in sharp contrast to current particle-based simulation techniques in which statistical sampling leads to computational cost that is proportional to Ma(-2), making calculations at small Ma very expensive. (c) 2005 American Institute of Physics.
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页码:1 / 4
页数:4
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