An approximate method in transport theory. II

Maxwell had constructed first approximate solutions of the basic slip problems in the rarefied gas flows by distinguishing between incident and outgoing distributions at a surface. He used a single parameter approximation to the incident distribution and a conservation relation. The method has been...

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Bibliographic Details
Published in:Physics of fluids (1994) 2006-11, Vol.18 (11), p.117106-117106-9
Main Authors: Loyalka, S. K., Naz, S.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fluid dynamics
Fundamental areas of phenomenology (including applications)
General theory
Physics
Rarefied gas dynamics
Slip flows
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Summary:Maxwell had constructed first approximate solutions of the basic slip problems in the rarefied gas flows by distinguishing between incident and outgoing distributions at a surface. He used a single parameter approximation to the incident distribution and a conservation relation. The method has been improved in the recent past through the use of two conservation relations and two-parameter approximations to the incident distribution. We have explored in this work a method to improve upon these latter approximations by using an arbitrary order parameter representation of the incident distribution. For a test problem, we have considered the Milne problem of one speed transport [S. K. Loyalka, Phys. Fluids 24, 1912 (1982)]. We have found that a three-parameter representation yields a result for extrapolation distance that is accurate to four figures. We have explored approximations up to order 512, and we have found that the accuracy of results is improved systematically with the order of the approximation, and results of any desired accuracy can be obtained.
ISSN:1070-6631
1089-7666
DOI:10.1063/1.2391736