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http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B75BX-4903KV6-1C5&_user=10&_coverDate=12%2F31%2F1988&_alid=760850276&_rdoc=4&_fmt=high&_orig=search&_cdi=12994&_sort=d&_docanchor=&view=c&_ct=76&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=c72960bb16e063310fe886e928457cf8#bibl1

USSR Computational Mathematics and Mathematical Physics
Volume 28, Issue 4, 1988, Pages 63-71

Comparative analysis of direct simulation algorithms in rarefied gas dynamics*1

M. S. Ivanov and S. V. Rogazinskii


Translated by Z.L.  Available online 2 July 2003.


Abstract
Following the general approach of the theory of Monte Carlo methods, we present a consistent construction of the direct simulation method for the “basic” N-particle kinetic equation. From the integral form of this equation we derive, under appropriate assumptions, approximate integral equations whose probabilistic interpretation is identical with the traditional direct simulation schemes used in rarefied gas dynamics. A comparative analysis of these schemes is carried out under the relevant conditions of applicability. An efficient “majorizing frequency” numerical scheme is proposed as an implementation of the direct simulation method for rarefied gas flows.