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Transonic Solutions for the Mach Reflection of Weak Shocks

  • Conference paper
IUTAM Symposium Transsonicum IV

Part of the book series: Fluid Mechanics and its Applications ((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.

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References

  1. K. G. Guderley, The Theory of Transonic Flow, Pergamon Press, Oxford, 1962.

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  2. J. K. Hunter, and M. Brio, Weak shock reflection, J. Fluid. Mech., 410 (2000), pp. 235–261.

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  3. A. M. Tesdall, and J. K. Hunter, Self-similar solutions for weak shock reflection, Siam. J. Appl. Math., 63 (2002), pp. 42–61.

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  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.

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  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. 193–205

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of California at Davis, Davis, California, 95616, USA

    J. K. Hunter & A. M. Tesdall

Authors
  1. J. K. Hunter
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  2. A. M. Tesdall
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Editor information

Editors and Affiliations

  1. DLR German Aerospace Center, Göttingen, Germany

    H. Sobieczky

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© 2003 Springer Science+Business Media Dordrecht

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Hunter, J.K., Tesdall, A.M. (2003). Transonic Solutions for the Mach Reflection of Weak Shocks. In: Sobieczky, H. (eds) IUTAM Symposium Transsonicum IV. Fluid Mechanics and its Applications, vol 73. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0017-8_2

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  • DOI: https://doi.org/10.1007/978-94-010-0017-8_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-3998-7

  • Online ISBN: 978-94-010-0017-8

  • eBook Packages: Springer Book Archive

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