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Macroscopic description of arbitrary Knudsen number flow using Boltzmann–BGK kinetic theory

Published online by Cambridge University Press:  15 February 2007

HUDONG CHEN ,
STEVEN A. ORSZAG  and
ILYA STAROSELSKY
HUDONG CHEN
Affiliation:
Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA
STEVEN A. ORSZAG
Affiliation:
Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA Department of Mathematics, P.O. Box 208283, Yale University, New Haven, CT 06520-8283, USA
ILYA STAROSELSKY
Affiliation:
Exa Corporation, 3 Burlington Woods Drive, Burlington, MA 01803, USA
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Abstract

We derive, without approximation, a closed-form macroscopic equation for finite Knudsen number flow using the Boltzmann–BGK kinetic theory with constant relaxation time. This general closed-form equation is specialized into a compact integro-differential equation for time-dependent isothermal unidirectional flows and results are presented for channel flow. This equation provides a clear demonstration of the effects of finite Knudsen number, and it also illustrates the limitations of the Boltzmann–BGK theory with constant relaxation time and bounce-back boundary conditions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 574 , 10 March 2007 , pp. 495 - 505
Copyright
Copyright © Cambridge University Press 2007

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References

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