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Shock Waves pp 1217-1222 | Cite as

Moment solution of comprehensive kinetic model for plane shock wave problem

  • R. Nagai
  • K. Maeno
  • H. Honma
  • A. Sakurai
Conference paper

Abstract

We consider the classic problem of a one-dimensional steady shock-wave solution of the Boltzmann kinetic equation utilizing a new type of 13-moment approximation proposed by Oguchi (1998). The model, unlike previous ones, expresses the collision term in an explicit function of the molecular velocity. We can thus obtain moment integrals directly because of its explicit expression. We can have five relations for five unknown functions to be determined as functions of the coordinate x. These can be reduced to a first-order differential equation that can be solved to provide the familiar smooth monotonie transition from the upstream supersonic state to the subsonic downstream state. Computed values of shock profile for various shock Mach numbers compare well with some existing results obtained by different models and methods to certain Mach numbers beyond which no solution exists.

Keywords

Mach Number Collision Term Shock Mach Number Boltzmann Kinetic Equation Molecular Velocity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    R. Becker: Z. f. Physik 8, 321 (1921)ADSCrossRefGoogle Scholar
  2. 2.
    H. Oguchi: ‘Comprehensive Kinetic Model for Weakly Rarefied Gases’. In: Rarefied Gas Dynamics, 23th Int. Symp. on Rarefied Gas Dynamics at Whistler, Canada, July 21–25, 2002 edited by E.P. Müntz, et al. (to be published)Google Scholar
  3. 3.
    H. Grad: Commun. Pure Appl. Math. 5, 257 (1952); Commun. Pure Appl. Math. 2, 325 (1949)CrossRefGoogle Scholar
  4. 4.
    H. Mott-Smith: Phys. Rev. 82, 885 (1951)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    A. Sakurai: J. Fluid Mech. 3, 255 (1957)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    K. Nanbu, Y. Watanabe: Rep. No. 366, Inst. High Speed Mech, Tohoku Univ. (1984)Google Scholar
  7. 7.
    R. Nagai, K. Maeno, H. Honma: In: Proc. on Symp. on Shock Waves Japan 2001 at Tsukuba, Japan, March 14–16, 2002, pp.597–600 (in Japanese)Google Scholar
  8. 8.
    E.A. Coddington, N. Levinoon: Theory of Ordinary Differential Equations, (McGraw-Hill, New York, 1955)Google Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • R. Nagai
    • 1
  • K. Maeno
    • 1
  • H. Honma
    • 1
  • A. Sakurai
    • 2
  1. 1.Chiba UniversityChibaJapan
  2. 2.Tokyo Denki UniversityTokyoJapan

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