Commun. Comput. Phys., 6 (2009), pp. 919-954.


Numerical Simulations of Rarefied Gases in Curved Channels: Thermal Creep, Circulating Flow, and Pumping Effect

Kazuo Aoki 1, Pierre Degond 2, Luc Mieussens 3*

1 Department of Mechanical Engineering and Science, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan.
2 Universite de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathematiques de Toulouse, F-31062 Toulouse, France; and CNRS, Institut de Mathematiques de Toulouse UMR 5219, F-31062 Toulouse, France.
3 Universite de Bordeaux, Institut de Mathematiques de Bordeaux, 351, cours de la Liberation, 33405 Talence cedex, France.

Received 4 November 2008; Accepted (in revised version) 1 April 2009
Available online 4 May 2009

Abstract

We present numerical simulations of a new system of micro-pump based on the thermal creep effect described by the kinetic theory of gases. This device is made of a simple smooth and curved channel with a periodic temperature distribution. Using the Boltzmann-BGK model as the governing equation for the gas flow, we develop a numerical method based on a deterministic finite volume scheme, implicit in time, with an implicit treatment of the boundary conditions. This method is comparatively less sensitive to the slow flow velocity than the usual Direct Simulation Monte Carlo method in case of long devices, and turns out to be accurate enough to compute macroscopic quantities like the pressure field in the channel. Our simulations show the ability of the device to produce a one-way flow that has a pumping effect.

AMS subject classifications: 76P05, 82B40, 82D05, 82C80, 65M06

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Key words: Knudsen compressor, thermal creep flow, transpiration flow, BGK model, implicit scheme.

*Corresponding author.
Email: aoki@aero.mbox.media.kyoto-u.ac.jp (K. Aoki), degond@mip.ups-tlse.fr (P. Degond), Luc.Mieussens@math.u-bordeaux1.fr (L. Mieussens)
 

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