## 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) |
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Pages (from-to) | 887-909 |

Number of pages | 23 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 76 |

Issue number | 3 |

DOIs | |

State | Published - 2016 |

### Bibliographical note

Publisher Copyright:© 2016 Society for Industrial and Applied Mathematics.

## Keywords

- Cellular detonation
- Detonation analog
- Detonation instability

## ASJC Scopus subject areas

- Applied Mathematics