Detonation shock dynamics and comparisons with direct numerical simulation

Comparisons between direct numerical simulation (DNS) of detonation and detonation shock dynamics (DSD) is made. The theory of DSD defines the motion of the detonation shock in terms of the intrinsic geometry of the shock surface, in particular for condensed phase explosives the shock normal velocity, D(n), the normal acceleration, D(n), and the total curvature, κ. In particular, the properties of three intrinsic front evolution laws are studied and compared. These are (i) constant speed detonation (Huygens construction), (ii) curvature-dependent speed propagation (D(n)-κ relation) and (iii) curvature-and speed-dependent acceleration (D(n)-D(n)-κ relation). We show that it is possible to measure shock dynamics directly from simulation of the reactive Euler equations and that subsequent numerical solution of the intrinsic partial differential equation for the shock motion (e.g. a D(n)-D(n)-κ relation) reproduces the computed shock motion with high precision.