Numerical Modeling of the Initiation of Reacting Shock Waves

  • Andrew Majda
  • Victor Roytburd
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)


The transition to detonation in gases is a very complicated multifaceted process. Turbulent mixing, interaction of acoustic waves with underlying chemical reactions, formation of regularly spaced Mach stem structures—this is just a partial list of phenomena taking part in the transition from deflagration to a self-sustained detonation. (See the review article [7] for an experimentalist’s summary). In this paper through carefully documented numerical experiments we investigate one aspect of the transition process which is also related to the direct initiation of reacting shock waves.


Detonation Wave Initial Pulse Compressible Euler Equation Brush Flame Direct Initiation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    G. E. Abouseif and T. Y. Toong. On direct initiation of gaseous detonations, Combust. Flame 45, 39–46 (1982).CrossRefGoogle Scholar
  2. 2.
    P. Colella, A. Majda, and V. Roytburd, Theoretical and numerical structure for reacting shock waves, SIAM J. Sci. Stat. Comput. 7, 1059–1080 (1986).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    W. Fickett and W. C. Davis, Detonation, University of California Press, Berkeley, 1979.Google Scholar
  4. 4.
    W. Fickett and W. W. Wood, Flow calculations for pulsating one-dimensional detonations, Phys. Fluids 9, 903–916 (1966).ADSCrossRefGoogle Scholar
  5. 5.
    T. Jackson and A. Kapila, Shock induced thermal runaway, SIAM J. Appl. Math. 45, 130–137 (1985).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    K. Kailasanath and E. S. Oran, Ignition of flamelets behind incident shock waves and the transition to detonation, Comb. Sci. Technol. 34, 345–362 (1983).CrossRefGoogle Scholar
  7. 7.
    J. H. Lee and I. O. Moen, Prog. Energy Combustion Science, 6, 359–389 (1980).CrossRefGoogle Scholar
  8. 8.
    C. L. Mader, Numerical Modeling of Detonations, University of California Press, Berkeley, 1979.zbMATHGoogle Scholar
  9. 9.
    A. Majda, High Mach number combustion, In Reacting Flows: Combustion and Chemical Reactors, AMS Lectures in Applied Mathematics, 24, 109–184 (1986).Google Scholar
  10. 10.
    A. Majda and R. Rosales, Nonlinear mean field — high frequency wave interactions in the induction zone, to appear in SIAM J. Appl. Math. (1987).Google Scholar
  11. 11.
    A. Majda and V. Roytburd, Detailed numerical simulation of transient behavior in reacting shock waves, (in preparation).Google Scholar
  12. 12.
    R. Rosales and A. Majda, Weakly nonlinear detonatiun waves, SIAM J. Appl. Math. 43, 1086–1118 (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • Andrew Majda
    • 1
  • Victor Roytburd
    • 2
  1. 1.Department of Mathematics and Program for Applied and Computational MathematicsPrinceton UniversityPrincetonUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations