TY - JOUR

T1 - Study of a model equation in detonation theory

T2 - Multidimensional effects

AU - Faria, Luiz

AU - Kasimov, A. R.

AU - Rosales, R. R.

N1 - Funding Information:
The work of this author was supported by King Abdullah University of Science and Technology (KAUST).
Publisher Copyright:
© 2016 Society for Industrial and Applied Mathematics.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Cellular detonation

KW - Detonation analog

KW - Detonation instability

UR - http://www.scopus.com/inward/record.url?scp=84976889291&partnerID=8YFLogxK

U2 - 10.1137/15M1039663

DO - 10.1137/15M1039663

M3 - Article

AN - SCOPUS:84976889291

SN - 0036-1399

VL - 76

SP - 887

EP - 909

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

IS - 3

ER -