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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 887-909 |
| Number of pages | 23 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 76 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jan 1 2016 |
Bibliographical note
KAUST Repository Item: Exported on 2021-07-06Acknowledgements: The 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.
Keywords
- Cellular detonation
- Detonation analog
- Detonation instability
ASJC Scopus subject areas
- Applied Mathematics