Study of a Model Equation in Detonation Theory: Multidimensional Effects
Name
Study of a Model Equation.pdf
Size
1.06 MB
Format
Adobe PDF
Checksum (MD5)
504e63eade18e3108a87799de9897509
Author(s)
Faria, Luiz
Kasimov, A. R.
Rosales, Rodolfo
Date Issued
May 2016
Journal
SIAM Journal on Applied Mathematics
Publisher
Society for Industrial and Applied Mathematics (SIAM)
Citation
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.
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/15M1039663
