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    Theory of weakly nonlinear self-sustained detonations

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    Type
    Article
    Authors
    Faria, Luiz cc
    Kasimov, Aslan R. cc
    Rosales, Rodolfo R.
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2015-11-03
    Online Publication Date
    2015-11-03
    Print Publication Date
    2015-12
    Embargo End Date
    2016-05-03
    Permanent link to this record
    http://hdl.handle.net/10754/622344
    
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    Abstract
    We 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.
    Citation
    Faria 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.
    Sponsors
    L.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.
    Publisher
    Cambridge University Press (CUP)
    Journal
    Journal of Fluid Mechanics
    DOI
    10.1017/jfm.2015.577
    arXiv
    1407.8466
    Additional Links
    https://dspace.mit.edu/bitstream/1721.1/116003/1/1407.8466.pdf
    ae974a485f413a2113503eed53cd6c53
    10.1017/jfm.2015.577
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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