The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems

A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve a collection of basic flow problems based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, two half-space problems, Kramers and thermal creep, and th...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2003-03, Vol.54 (2), p.273-303
Main Author: Siewert, C. E.
Format: Article
Language:English
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Summary:A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve a collection of basic flow problems based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, two half-space problems, Kramers and thermal creep, and three problems defined by flow in a plane-parallel channel, Poiseuille, thermal-creep and Couette flow, are solved (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.
ISSN:0044-2275
1420-9039
DOI:10.1007/s000330300005