STUDY OF A MODEL EQUATION IN DETONATION THEORY: MULTIDIMENSIONAL EFFECTS
KAUST DepartmentApplied Mathematics and Computational Science Program
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Permanent link to this recordhttp://hdl.handle.net/10754/670014
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AbstractWe extend the reactive Burgers equation presented in [A. R. Kasimov, L. M. Faria, and R. R. Rosales, Phys. Rev. Lett., 110 (2013), 104104], [L. M. Faria, A. R. Kasimov, and R. R. Rosales, SIAM J. Appl. Math., 74 (2014), pp. 547-570] to include multidimensional effects. Furthermore, we explain how the model can be rationally justified following the ideas of the asymptotic theory developed in [L. M. Faria, A. R. Kasimov, and R. R. Rosales, J. Fluid Mech., 784 (2015), pp. 163-198]. The proposed model is a forced version of the unsteady small disturbance transonic flow equations. We show that for physically reasonable choices of forcing functions, traveling wave solutions akin to detonation waves exist. It is demonstrated that multidimensional effects play an important role in the stability and dynamics of the traveling waves. Numerical simulations indicate that solutions of the model tend to form multidimensional patterns analogous to cells in gaseous detonations.
CitationFaria, L. M., Kasimov, A. R., & Rosales, R. R. (2016). Study of a Model Equation in Detonation Theory: Multidimensional Effects. SIAM Journal on Applied Mathematics, 76(3), 887–909. doi:10.1137/15m1039663
SponsorsThe work of LMF and ARK was supported by King Abdullah University of Science and Technology (KAUST). The work of RRR was partially supported by NSF grants DMS-1115278 and DMS-1318942.