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Macroscopic description of arbitrary Knudsen number flow using Boltzmann–BGK kinetic theory. Part 2

Published online by Cambridge University Press:  16 June 2010

HUDONG CHEN ,
STEVEN A. ORSZAG  and
ILYA STAROSELSKY
HUDONG CHEN
Affiliation:
Exa Corporation, 55 Network Drive, Burlington, MA 01803, USA
STEVEN A. ORSZAG*
Affiliation:
Exa Corporation, 55 Network 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, 55 Network Drive, Burlington, MA 01803, USA
*
†Email address for correspondence: steven.orszag@yale.edu
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Abstract

We extend our previous analysis of closed-form equations for finite Knudsen number flow and scalar transport that result from the Boltzmann–Bhatnagar–Gross–Krook (BGK) kinetic theory with constant relaxation time. Without approximation, we obtain closed-form equations for arbitrary spatial dimension and flow directionality which are local differential equations in space and integral equations in time. These equations are further simplified for incompressible flow and scalars. The particular case of no-flow scalar transport admits analytical solutions that exhibit ballistic behaviour at short times while behaving diffusively at long times. It is noteworthy that, even with constant relaxation time BGK microphysics, quite complex macroscopic descriptions result that would be difficult to obtain using classical constitutive models or continuum averaging.

JFM classification

Mathematical Foundations: General fluid mechanics Micro-/Nano-fluid dynamics: Non-continuum effects Non-Newtonian Flows: Non-Newtonian Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 658 , 10 September 2010 , pp. 294 - 309
Copyright
Copyright © Cambridge University Press 2010

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References

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