Axisymmetric Shock-Attached Frame Detonation Simulations

We present a method of simulating one-dimensional axisymmetric detonations governed by the reactive Euler equations in a reference frame moving with the shock surface. We use this methodology to verify relations between normal detonation speed, $D_n$, and curvature, ($\kappa$), as predicted by Detonation Shock Dynamics (DSD), an asymptotic theory derived in the limit of slowly varying, weakly curved detonations. Our simulations demonstrate the previously theorized instability of certain regions of $D_n$-$\kappa$ solutions with multiple turning points, which result in rapid transition to strong detonation or failure of the reaction front. It is also shown that the shock-attached frame method can be used to obtain $D_n$-$\kappa$ relations that satisfy the complete reactive Euler equations without restrictions to small curvature or near Chapman-Jouguet detonation speeds.