KAUST DepartmentApplied Mathematics and Computational Science Program
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AbstractWe propose a theory of weakly nonlinear multidimensional self-sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced unsteady small-disturbance transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multidimensional detonations.
CitationFaria LM, Kasimov AR, Rosales RR (2015) Theory of weakly nonlinear self-sustained detonations. Journal of Fluid Mechanics 784: 163–198. Available: http://dx.doi.org/10.1017/jfm.2015.577.
SponsorsL.M.F. and A.R.K. gratefully acknowledge research support by King Abdullah University of Science and Technology (KAUST). The research by R.R.R. was partially supported by NSF grants DMS-1007967, DMS-1115278, DMS-1318942, and by KAUST during his research visit to KAUST in November 2013. L.M.F. would like to thank S. Korneev and D. Ketcheson for their help with numerical computations.
PublisherCambridge University Press (CUP)
JournalJournal of Fluid Mechanics