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Theoretical and Computational Fluid Dynamics

, Volume 8, Issue 5, pp 365–375 | Cite as

Entropy jump across an inviscid shock wave

  • Manuel D. Salas
  • Angelo Iollo
Article

Abstract

The Shock jump conditions for the Euler equations in their primitive form are derived by using generalized functions. The shock profiles for specific volume, speed, and pressure and shown to be the same, however, density has a different shock profile. Careful study of the equations that govern the entropy shows that the inviscid entropy profile has a local maximum within the shock layer. We demonstrate that because of this phenomenon, the entropy propagation equation cannot be used as a conservation law.

Keywords

Entropy Shock Wave Local Maximum Euler Equation Propagation Equation 
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]
    Becker, R. (1922). Stosswelle und detonation. Zeitschrift für Physik, 8, 321–362.Google Scholar
  2. [2]
    Colombeau, J.F. (1990). Multiplication of distributions. Bulletin of the American Mathematical Society, 23, 2.Google Scholar
  3. [3]
    Colombeau, J.F., and Le Roux, A.Y. (1986). Numerical Techniques in Elastodynamics. Lectures Notes in Mathematics, vol. 1270, Springer-Verlag, Berlin, pp. 104–114.Google Scholar
  4. [4]
    Colombeau, J.F., and Le Roux, A.Y. (1988). Multiplications of distributions in elasticity and hydrodynamics. Journal of Mathematial Physics, 29, 2.Google Scholar
  5. [5]
    Farassat, F. (1994). An Introduction to Generalized Functions with Some Applications in Aerodynamics and Aeroacoustics. NASA TP-3428.Google Scholar
  6. [6]
    Hugoniot, H. (1889). Sur la propagation du mouvement dans les corps et spécialement dans les gaz parfaits. Journal de l'école polytechnique, 58, 1125.Google Scholar
  7. [7]
    Morduchow, M., and Libby, P. (1949). On a complete solution of the one-dimensional flow equations of a viscous, heat conducting, compressible gas. Journal of the Aeronautical Sciences, Nov., 674–684.Google Scholar
  8. [8]
    Rankine, W.J.M. (1870). On the thermodynamic theory of waves of finite longitudinal disturbances. Transactions of the Royal Society of London, 160, 277–288.Google Scholar
  9. [9]
    Richards, I.J., and Youn, H.K. (1990). Theory of Distributions. Cambridge University Press, Cambridge.Google Scholar
  10. [10]
    Smoller, J. (1983). Shock Waves and Reaction—Diffusion Equations. Springer-Verlag, New York.Google Scholar
  11. [11]
    Stokes, G.G. (1848). On a difficulty in the theory of sound. Philosophical Magazine, 3(33), 349–356.Google Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Manuel D. Salas
    • 1
  • Angelo Iollo
    • 2
  1. 1.NASA Langley Research CenterHamptonUSA
  2. 2.Dipartimento di Ingegneria Aeronautica e SpazialePolitecnico di TorinoTorinoItaly

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