Mathematical modelling of the concave front in the adjacent high explosive detonation problem

This study presents an analysis of the transition-zone in adjacent high explosive (HE) detonation problems which uses a D,κ,D˙ relationship, where D is the detonation front-normal velocity, κ is the detonation front curvature and D˙ is the time derivative of detonation front-normal velocity. Our approach extends the traditional (D,κ) model to accurately predict the behaviour of both diverging and converging detonation shock fronts. Our findings affirm that a hyperbolic type of front evolution equation, enhanced with wave acceleration, provides a robust framework for modelling complex shock front dynamics in HE materials. This approach not only captures the natural effects of straightness and boundary slope jumps in the transition-zone but also bridges the gap between mathematical predictions and experimental observations, offering insights into the behaviour of both diverging and converging detonation propagations in a homogeneous HE.