Skip to main content
Log in

Evolution and interaction of a characteristic shock with an acceleration wave in a reacting gas

  • Published:
Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we consider the evolution and propagation of a characteristic shock through a reacting gas and studied its interaction with an acceleration wave. A particular solution to the governing system, which exhibits space-time dependence, has been considered to study the evolutionary behavior of the characteristic shock. The amplitudes of the reflected and transmitted waves and the jump in shock acceleration, influenced by the incident wave amplitude after interaction are evaluated.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Mentrelli, T. Ruggeri, M. Sugiyama and N. Zhao, Wave Motion 45, 498 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  2. P. D. Lax, Comm. Pure Appl. Math. 10, 537 (1957).

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Boillat and T. Rugerri, Bolletino U. M. I. 15A, 197 (1978).

    Google Scholar 

  4. A. Jeffrey, Applicable Analysis 3, 79 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  5. G. Boillat and T. Rugerri, Proc. Roy. Soc. Edin. 83A, 17 (1979).

    Article  Google Scholar 

  6. E. Varley and E. Cumberbatch, J. Inst. Math. Applics. 1, 101 (1965).

    Article  MathSciNet  Google Scholar 

  7. T. Rugerri, Applicable Analysis 11, 103 (1980).

    Article  MathSciNet  Google Scholar 

  8. A. Jeffrey, Quasilinear hyperbolic systems and waves (Pitman, London, 1976).

    MATH  Google Scholar 

  9. G. Boillat and T. Rugerri, Wave Motion 1, 149 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  10. L. Landau and E. Lifchith, Fluid Mechanics (Pergamon Press, 1959).

    Google Scholar 

  11. L. Brun, Ondes de choc finies dans les solides elastiques, in Mechanical waves in solids, Ed. by J. Mandel and L. Brun (Springer, 1975).

    Google Scholar 

  12. Ch. Radha, V. D. Sharma, and A. Jeffrey, Applicable Analysis 50, 145 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Jena, Applicable Analysis 84(1), 37 (2005).

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Jena, Z. Angew. Math. Phys. (ZAMP) 58, 416 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  15. N. Virgopia and F. Ferraioli, Continuum Mech. Thermodyn. 6, 31 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  16. F. Conforto, J. Math. Anal. Appl. 253, 459 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Jena, Theor. Comput. Fluid Dyn. 22, 145 (2008).

    Article  MATH  Google Scholar 

  18. J. Jena and V. D. Sharma, J. Eng. Math. 60, 43 (2007).

    Article  MathSciNet  Google Scholar 

  19. Manoj Pandey and V. D. Sharma, Wave Motion 44, 346 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhen-Huan Teng, A. J. Chorin, and Tai-Ping Liu, SIAM J. Appl. Math. 42(5), 964 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  21. G. I. Barenblatt, A. J. Chorin, and A. Kast, Proc. Natl. Acad. Sci. USA 94(51), 2762 (1997).

    Google Scholar 

  22. Ying Lung-An and Wang Ching-Hua, Trans. American Math. Soc. 266(2), 363 (1981).

    Article  Google Scholar 

  23. M. Torrisi, J. Appl. Math. and Phys. (ZAMP) 38, 117 (1987).

    Article  MATH  Google Scholar 

  24. M. Torrisi, J. Engg. Math. 22 239 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  25. C. Harle, G. F. Carey, and P. L. Varghese, Int. J. Num. Meth. in Fluids 32, 691 (2000).

    Article  MathSciNet  Google Scholar 

  26. E. Godlewski and P. A. Raviart, Numerical approximations of hyperbolic systems of conservations laws (Springer-Verlag, New York, 1996).

    Book  Google Scholar 

  27. V. D. Sharma, R. Ram, and P. Sachdev, J. FluidMech. 185, 153 (1987).

    Article  MATH  Google Scholar 

  28. J. F. Clarke, J. Fluid Mech. 89, 343 (1978).

    Article  MATH  Google Scholar 

  29. G. J. Pert, J. Fluid Mech. 100, 257 (1980).

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Courant and K. O. Friedrichs, Supersonic flow and shock waves (Springer, New York, 1999).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Randheer Singh.

Additional information

(Submitted by A. M. Elizarov)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Singh, R., Jena, J. Evolution and interaction of a characteristic shock with an acceleration wave in a reacting gas. Lobachevskii J Math 34, 248–255 (2013). https://doi.org/10.1134/S1995080213030104

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995080213030104

Keywords and phrases

Navigation