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Theory of detonation with an embedded sonic locus

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Title: Theory of detonation with an embedded sonic locus
Author(s): Stewart, D. Scott; Kasimov, Aslan R.
Abstract: We address the problem of generalizing sonic conditions to a three-dimensional unsteady self-sustained detonation wave. The conditions are shown 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.
Issue Date: 2004-10
Publisher: Department of Theoretical and Applied Mechanics (UIUC)
Series/Report: TAM Reports 1053, (2004)
Genre: Technical Report
Type: Text
Language: English
ISSN: 0073-5264
Publication Status: published or submitted for publication
Peer Reviewed: is peer reviewed
Date Available in IDEALS: 2007-03-09
Is Version Of: Published as: D. Scott Stewart and Aslan R. Kasimov. Theory of detonation with an embedded sonic locus. SIAM Journal on Applied Mathematics, Vol. 66, No. 2, 2006, pp. 384-407. DOI: 10.1137/040616930. Copyright 2006 Society for Industrial and Applied Mathematics. Also available at:

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  • Theoretical and Applied Mechanics (TAM) Technical Reports
    TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.

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