Study of a Model Equation in Detonation Theory: Multidimensional Effects
Résumé
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. Fur-thermore, we explain how the model can be rationally justified following the ideas of the asymptotictheory 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 transonicflow equations. We show that for physically reasonable choices of forcing functions, traveling wavesolutions akin to detonation waves exist. It is demonstrated that multidimensional effects play animportant role in the stability and dynamics of the traveling waves. Numerical simulations indicatethat solutions of the model tend to form multidimensional patterns analogous to cells in gaseousdetonations.