Theory of detonation with an embedded sonic locus

D. Scott Stewart*, Aslan R. Kasimov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


A steady planar self-sustained detonation has a sonic surface in the reaction zone that resides behind the lead shock. In this work we address the problem of generalizing sonic conditions for a three-dimensional unsteady self-sustained detonation wave. The conditions are proposed to be the characteristic compatibility conditions on the exceptional surface of the governing hyperbolic system of reactive Euler equations. Two equations are derived that are necessary to determine the motion of both the lead shock and the sonic surface. Detonation with an embedded sonic locus is thus treated as a two-front phenomenon: a reaction zone whose domain of influence is bounded by two surfaces, the lead shock surface and the trailing characteristic surface. The geometry of the two surfaces plays an important role in the underlying dynamics. We also discuss how the sonic conditions of detonation stability theory and detonation shock dynamics can be obtained as special cases of the general sonic conditions.

Original languageEnglish (US)
Pages (from-to)384-407
Number of pages24
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2006
Externally publishedYes


  • Chemically reacting flows
  • Shocks and singularities
  • Supersonic flows
  • Transonic flows

ASJC Scopus subject areas

  • Applied Mathematics


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