Shock Waves

, Volume 26, Issue 2, pp 141–160 | Cite as

Set-valued solutions for non-ideal detonation

  • R. Semenko
  • L. M. Faria
  • A. R. Kasimov
  • B. S. Ermolaev
Original Article


The existence and structure of a steady-state gaseous detonation propagating in a packed bed of solid inert particles are analyzed in the one-dimensional approximation by taking into consideration frictional and heat losses between the gas and the particles. A new formulation of the governing equations is introduced that eliminates the difficulties with numerical integration across the sonic singularity in the reactive Euler equations. With the new algorithm, we find that when the sonic point disappears from the flow, there exists a one-parameter family of solutions parameterized by either pressure or temperature at the end of the reaction zone. These solutions (termed “set-valued” here) correspond to a continuous spectrum of the eigenvalue problem that determines the detonation velocity as a function of a loss factor.


Gaseous detonation Heat and momentum losses Velocity deficit 



The research reported in this publication was supported by the King Abdullah University of Science and Technology (KAUST).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • R. Semenko
    • 1
    • 3
  • L. M. Faria
    • 1
    • 4
  • A. R. Kasimov
    • 1
  • B. S. Ermolaev
    • 2
  1. 1.Applied Mathematics and Computational ScienceKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Semenov Institute of Chemical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Department of Mechanics and MathematicsNovosibirsk State UniversityNovosibirskRussia
  4. 4.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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