Shock Waves

, 18:193 | Cite as

A numerical study of oblique shock wave reflections over wedges in an ideal quantum gas

  • J. C. Huang
  • T. Y. Hsieh
  • J. Y. Yang
  • K. Takayama
Original Article
First Online:
Received:
Revised:
Accepted:

Abstract

The various oblique shock wave reflection patterns generated by a moving incident shock on a planar wedge using an ideal quantum gas model are numerically studied using a novel high resolution quantum kinetic flux splitting scheme. With different incident shock Mach numbers and wedge angles as flow parameters, four different types of reflection patterns, namely, the regular reflection, simple Mach reflection, complex Mach reflection and the double Mach reflection as in the classical gas can be classified and observed. Both Bose–Einstein and Fermi–Dirac gases are considered.

Keywords

Shock wave reflection Quantum gas dynamics Wedge High resolution scheme 

PACS

51.10.+y 67.10.-j 
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References

  1. 1.
    Ben-Dor G. (1992). Shock wave reflection phenomena. Springer, New-York MATHGoogle Scholar
  2. 2.
    Bhatnagar P.L., Gross E.P. and Krook M. (1954). A model for collision process in gases I: small amplitude processes in charged and neutral one component systems. Phys. Rev. 94: 511–525 MATHCrossRefGoogle Scholar
  3. 3.
    Chapman S. and Cowling T.G. (1970). The mathematical theory of non-uniform gases. Cambridge University Press, London Google Scholar
  4. 4.
    Chou S.Y. and Baganoff D. (1997). Kinetic flux-vector splitting for the Navier-Stokes equations. J. Comput. Phys. 130: 217–230 MATHCrossRefGoogle Scholar
  5. 5.
    Deshpande, S.M.: A second order accurate, kinetic-theory based, method for inviscid compressible flows. NASA Langley Technical Paper No. 2613 (1986)Google Scholar
  6. 6.
    Glaz H.M., Collella P., Glass I.I. and Deschambault R.L. (1985). A numerical study of oblique shock-wave reflections with experimental comparisons. Proc. R. Soc. Lond. A398: 117–140 Google Scholar
  7. 7.
    Hirsch C. (1988). Numerical computation of internal and external flows. Wiley, New York MATHGoogle Scholar
  8. 8.
    Huang K. (1987). Statistical mechanics. Wiley, New York MATHGoogle Scholar
  9. 9.
    Jiang G.-S. and Shu C.-W. (1996). Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126: 202–228 MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kadanoff L.P. and Baym G. (1962). Quantum statistical mechanics, Chap. 6. Benjamin, New York Google Scholar
  11. 11.
    Liu X.-D., Osher S. and Chan T. (1994). Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115: 200–212 MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Ohwada T. (2002). On the construction of kinetic schemes. J. Comput. Phys. 177: 156–175 MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Pathria, R.K.: Statistical mechanics, 2nd edn. Butterworth-Heinemann (1996)Google Scholar
  14. 14.
    Patterson G.N. (1971). Introduction to the kinetic theory of gas flows. University of Toronto Press, Toronto Google Scholar
  15. 15.
    Sanders R.H. and Predergast K.H. (1974). The possible relation of the 3-kiloparsec arm to explosions in the galactic nucleus. Astrophys. J. 188: 489 CrossRefGoogle Scholar
  16. 16.
    Takayama K. and Jiang Z. (1997). Shock wave reflection over wedges: a benchmark test of CFD and experiments. Shock Waves 7: 191–203 MATHCrossRefGoogle Scholar
  17. 17.
    Toro E.F. (1999). Riemann solvers and numerical methods for fluid dynamics. Springer, Berlin MATHGoogle Scholar
  18. 18.
    Uehling E.A. and Uhlenbeck G.E. (1933). Transport phenomena in Bose-Einstein and Fermi-Dirac gases. I. Phys. Rev. 43: 552 MATHCrossRefGoogle Scholar
  19. 19.
    Xu K. and Prendergast K.H. (1994). Numerical Navier-Stokes solutions from gas kinetic theory. J. Comput. Phys. 114: 9–17 MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Xu, K.: Gas-kinetic schemes for unsteady compressible flow simulations. In: Proceedings of the 29th Computational Fluid Dynamics Lecture Series, von Karman Institute for Fluid Dynamics, Rhode-Saint-Geneses. Belgium (1998)Google Scholar
  21. 21.
    Xu K. (2001). A gas-kinetic BGK scheme for the Navier-Stokes equations and its connection with artificial dissipation and Godunov method. J. Comput. Phys. 171: 289–335 MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Yang J.Y. and Shi Y.H. (2006). A kinetic beam scheme for ideal quantum gas dynamics. Proc. R. Soc. Lond A 462: 1553–1572 MATHMathSciNetGoogle Scholar
  23. 23.
    Yang J.Y., Hsieh T.Y. and Shi Y.H. (2007). Kinetic flux splitting schemes for ideal quantum gas dynamics. SIAM J. Scient. Comput. 29(1): 221–244 MATHMathSciNetCrossRefGoogle Scholar
  24. 24.
    Yang J.Y., Hsieh T.Y., Shi Y.H. and Xu K. (2007). High order kinetic flux splitting schemes in general coordinates for ideal quantum gas dynamics. J. Comput. Phys. 227: 967–982 MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • J. C. Huang
    • 1
  • T. Y. Hsieh
    • 2
  • J. Y. Yang
    • 2
  • K. Takayama
    • 3
  1. 1.Merchant Marine DepartmentNational Taiwan Ocean UniversityKeelungTaiwan, ROC
  2. 2.Institute of Applied MechanicsNational Taiwan UniversityTaipeiTaiwan, ROC
  3. 3.Institute of Fluid SciencesTohoku UniversitySendaiJapan

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