Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems

Kazuo Aoki[1]; Tetsuro Tsuji[2]

  • [1] Department of Mechanical Engineering and Science Kyoto University Japan
  • [2] Department of Mechanical Science and Bioengineering Osaka University Japan

Séminaire Laurent Schwartz — EDP et applications (2013-2014)

  • page 1-13
  • ISSN: 2266-0607

Abstract

top
Unsteady flows of a rarefied gas in a full space caused by an oscillatory motion of an infinitely wide plate in its normal direction is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The present notes aim at showing the properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting.

How to cite

top

Aoki, Kazuo, and Tsuji, Tetsuro. "Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems." Séminaire Laurent Schwartz — EDP et applications (2013-2014): 1-13. <http://eudml.org/doc/275778>.

@article{Aoki2013-2014,
abstract = {Unsteady flows of a rarefied gas in a full space caused by an oscillatory motion of an infinitely wide plate in its normal direction is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The present notes aim at showing the properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting.},
affiliation = {Department of Mechanical Engineering and Science Kyoto University Japan; Department of Mechanical Science and Bioengineering Osaka University Japan},
author = {Aoki, Kazuo, Tsuji, Tetsuro},
journal = {Séminaire Laurent Schwartz — EDP et applications},
language = {eng},
pages = {1-13},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems},
url = {http://eudml.org/doc/275778},
year = {2013-2014},
}

TY - JOUR
AU - Aoki, Kazuo
AU - Tsuji, Tetsuro
TI - Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2013-2014
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
SP - 1
EP - 13
AB - Unsteady flows of a rarefied gas in a full space caused by an oscillatory motion of an infinitely wide plate in its normal direction is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The present notes aim at showing the properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting.
LA - eng
UR - http://eudml.org/doc/275778
ER -

References

top
  1. C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, Berlin, 1988). Zbl0646.76001MR1313028
  2. Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston, 2002); see also http://hdl.handle.net/2433/66099. Zbl1021.76002MR1919070
  3. Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhäuser, Boston, 2007); see also http://hdl.handle.net/2433/66098. Zbl1144.76001MR2274674
  4. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford Univ. Press, Oxford, 1994). MR1352466
  5. Y. Sone and S. Takata, Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layer at the bottom of the Knudsen layer, Transp. Theory Stat. Phys. 21, 501–530 (1992). Zbl0793.76078
  6. T. Tsuji and K. Aoki, Numerical analysis of nonlinear acoustic wave propagation in a rarefied gas, in 28th International Symposium on Rarefied Gas Dynamics 2012, AIP Conf. Proc. 1501, edited by M. Mareschal and A. Santos (AIP, Melville, 2012), pp. 115–122. 
  7. T. Tsuji and K. Aoki, Moving boundary problems for a rarefied gas: Spatially one-dimensional case, J. Comp. Phys. 250, 574–600 (2013). MR3079550
  8. P.L. Bhatnagar, E.P. Gross, M. Krook, A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94, 511–525 (1954). Zbl0055.23609
  9. P. Welander, On the temperature jump in a rarefied gas, Ark. Fys. 7, 507–553 (1954). Zbl0057.23301MR62041
  10. K. Aoki, Y. Sone, K. Nishino, and H. Sugimoto, Numerical analysis of unsteady motion of a rarefied gas caused by sudden changes of wall temperature with special interest in the propagation of a discontinuity in the velocity distribution function, in Rarefied Gas Dynamics, edited by A. E. Beylich (VCH, Weinheim, 1991) 222–231. 
  11. T. Tsuji and K. Aoki, Gas motion in a microgap between a stationary plate and a plate oscillating in its normal direction,” Microfluid. Nanofluid. 16, 1033–1045 (2014). 
  12. T. Tsuji, K. Aoki, Decay of an oscillating plate in a free-molecular gas, in 27th International Symposium on Rarefied Gas Dynamics 2010, AIP Conf. Proc. 1333, edited by D.A. Levin, I.J. Wysong, and A.L. Garcia (AIP, Melville, 2011), pp. 140–145. 
  13. T. Tsuji, K. Aoki, Decay of a linear pendulum in a free-molecular gas and in a special Lorentz gas, J. Stat. Phys. 146, 620–645 (2012). Zbl1245.82066MR2880035
  14. S. Caprino, G. Cavallaro, C. Marchioro, On a microscopic model of viscous friction, Math. Models Methods Appl. Sci. 17,1369–1403 (2007). Zbl1216.70008MR2353147
  15. G. Russo and F. Filbet, Semilagrangian schemes applied to moving boundary problems for the BGK model of rarefied gas dynamics, Kinet. Relat. Models 2, 231 (2009). Zbl05643199MR2472158
  16. T. Tsuji and K. Aoki, Decay of a linear pendulum in a collisional gas: Spatially one-dimensional case, Phys. Rev. E, 89, 052129 (2014). 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.