TY - JOUR

T1 - STUDY OF A MODEL EQUATION IN DETONATION THEORY: MULTIDIMENSIONAL EFFECTS

AU - Faria, L. M.

AU - Kasimov, Aslan R.

AU - Rosales, R. R.

N1 - KAUST Repository Item: Exported on 2021-07-06
Acknowledgements: 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.

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.

UR - http://hdl.handle.net/10754/670014

UR - http://epubs.siam.org/doi/10.1137/15M1039663

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

U2 - 10.1137/15M1039663

DO - 10.1137/15M1039663

M3 - Article

VL - 76

SP - 887

EP - 909

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 1095-712X

IS - 3

ER -