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Abstract
We propose a new test method for investigating which macroscopic continuum models, among the many existing models, give the best description of rarefied gas flows over a range of Knudsen numbers. The merits of our method are: no boundary conditions for the continuum models are needed, no coupled governing equations are solved, while the Knudsen layer is still considered. This distinguishes our proposed test method from other existing techniques (such as stability analysis in time and space, computations of sound speed and dispersion, and the shock wave structure problem). Our method relies on accurate, essentially noisefree, solutions of the basic microscopic kinetic equation, e.g. the Boltzmann equation or a kinetic model equation; in this paper, the BGK model and the ESBGK model equations are considered. Our method is applied to test whether onedimensional stationary Couette flow is accurately described by the following macroscopic transport models: the NavierStokesFourier equations, Burnett equations, Grad's 13 moment equations, and the regularized 13 moment equations (two types: the original, and that based on an order of magnitude approach). The gas molecular model is Maxwellian.
For Knudsen numbers in the transitioncontinuum regime (Kn lessthanorequals, slant 0.1), we find that the two types of regularized 13 moment equations give similar results to each other, which are better than Grad's original 13 moment equations, which, in turn, give better results than the Burnett equations. The NavierStokesFourier equations give the worst results. This is as expected, considering the presumed accuracy of these models. For cases of higher Knudsen numbers, i.e. Kn > 0.1, all macroscopic continuum equations tested fail to describe the flows accurately. We also show that the above conclusions from our tests are general, and independent of the kinetic model used.
Original language  English 

Pages (fromto)  748769 
Number of pages  21 
Journal  Journal of Computational Physics 
Volume  218 
Issue number  2 
DOIs  
Publication status  Published  1 Nov 2006 
Keywords
 noncontinuum effects
 rarefied gas flows
 microfluidics
 burnett equations
 moment equations
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Projects
 1 Finished

Fluid Flow and Heat Transfer in Gas Microsystems
Reese, J.
EPSRC (Engineering and Physical Sciences Research Council)
1/01/04 → 30/09/07
Project: Research