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.
@article{SLSEDP_2013-2014____A6_0,
author = {Aoki, Kazuo and Tsuji, Tetsuro},
title = {Moving boundary problems in kinetic theory of gases: {Spatially} one-dimensional problems},
journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
note = {talk:6},
pages = {1--13},
publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
year = {2013-2014},
doi = {10.5802/slsedp.52},
language = {en},
url = {http://www.numdam.org/articles/10.5802/slsedp.52/}
}
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 N1 - talk:6 PY - 2013-2014 SP - 1 EP - 13 PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://www.numdam.org/articles/10.5802/slsedp.52/ DO - 10.5802/slsedp.52 LA - en ID - SLSEDP_2013-2014____A6_0 ER -
%0 Journal Article %A Aoki, Kazuo %A Tsuji, Tetsuro %T Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems %J Séminaire Laurent Schwartz — EDP et applications %Z talk:6 %D 2013-2014 %P 1-13 %I Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique %U http://www.numdam.org/articles/10.5802/slsedp.52/ %R 10.5802/slsedp.52 %G en %F SLSEDP_2013-2014____A6_0
Aoki, Kazuo; Tsuji, Tetsuro. Moving boundary problems in kinetic theory of gases: Spatially one-dimensional problems. Séminaire Laurent Schwartz — EDP et applications (2013-2014), Exposé no. 6, 13 p. doi : 10.5802/slsedp.52. http://www.numdam.org/articles/10.5802/slsedp.52/
[1] C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, Berlin, 1988). | MR | Zbl
[2] Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston, 2002); see also http://hdl.handle.net/2433/66099. | MR | Zbl
[3] Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhäuser, Boston, 2007); see also http://hdl.handle.net/2433/66098. | MR | Zbl
[4] G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford Univ. Press, Oxford, 1994). | MR
[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). | Zbl
[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). | MR
[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). | Zbl
[9] P. Welander, On the temperature jump in a rarefied gas, Ark. Fys. 7, 507–553 (1954). | MR | Zbl
[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). | MR | Zbl
[14] S. Caprino, G. Cavallaro, C. Marchioro, On a microscopic model of viscous friction, Math. Models Methods Appl. Sci. 17,1369–1403 (2007). | MR | Zbl
[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). | MR
[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).
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