Detonation waves and the front tracking method

Detonation waves dominate the fluid flow in an explosive material. For numerical simulations, there is a need to account for the important properties of a propagating detonation wave without the fine grid necessary to resolve the very narrow reaction zone. The effects of the dynamics within the reaction zone on the fluid state behind the detonation wave are discussed. In contrast to a shock wave, the behavior of a detonation wave depends on the front curvature. Moreover, the flow behind a diverging underdriven detonation wave is supersonic relative to the front. This leads to composite waves and split waves which are analogous to those that occur for a fluid with a nonconvex equation of state. The wave structure and the wave curve for both converging and diverging detonation waves are described. The wave curve allows numerical calculations using the front tracking method to model multidimensional detonation problems. Implementing the analytic wave structure in numerical calculations is discussed.