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Transonic Solutions for the Mach Reflection of Weak Shocks

  • J. K. Hunter
  • A. M. Tesdall
Part of the Fluid Mechanics and its Applications book series (FMIA, volume 73)

Abstract

We present numerical solutions of the steady and unsteady transonic small disturbance equations that describe the Mach reflection of weak shock waves. The solutions contain a complex structure consisting of a sequence of triple points and tiny supersonic patches directly behind the leading triple point, formed by the reflection of weak shocks and expansion waves between the sonic line and the Mach shock. The presence of an expansion fan at each triple point resolves the von Neumann paradox. The numerical results and theoretical considerations suggest that there may be an infinite sequence of triple points in an inviscid weak shock Mach reflection.

Keywords

von Neumann paradox weak shock Mach reflection self-similar solutions 

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References

  1. [1]
    K. G. Guderley, The Theory of Transonic Flow, Pergamon Press, Oxford, 1962.Google Scholar
  2. [2]
    J. K. Hunter, and M. Brio, Weak shock reflection, J. Fluid. Mech., 410 (2000), pp. 235–261.MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. [3]
    A. M. Tesdall, and J. K. Hunter, Self-similar solutions for weak shock reflection, Siam. J. Appl. Math., 63 (2002), pp. 42–61.MathSciNetzbMATHCrossRefGoogle Scholar
  4. [4]
    E. I. Vasil’ev, and A. N. Kraiko, Numerical simulation of weak shock diffraction over a wedge under the von Neumann paradox conditions, Computational Mathematics and Mathematical Physics, 39 (1999), pp. 1335–1345.MathSciNetGoogle Scholar
  5. [5]
    A. R. Zakharian, M. Brio, J. K. Hunter, AND G. Webb, The von Neumann paradox in weak shock reflection, J. Fluid. Mech., 422 (2000), pp. 193–205MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • J. K. Hunter
    • 1
  • A. M. Tesdall
    • 1
  1. 1.Department of MathematicsUniversity of California at DavisDavisUSA

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