Study of a Model Equation in Detonation Theory: Multidimensional Effects
Author(s)Faria, Luiz; Kasimov, A. R.; Rosales, Rodolfo
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We 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
SIAM Journal on Applied Mathematics
Society for Industrial and Applied Mathematics (SIAM)
Faria, L. M., A. R. Kasimov, and R. R. Rosales. “Study of a Model Equation in Detonation Theory: Multidimensional Effects.” SIAM Journal on Applied Mathematics 76, no. 3 (January 2016): 887–909. © 2016, Society for Industrial and Applied Mathematics.
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