Program burn algorithms based on detonation shock dynamics: Discrete approximations of detonation flows with discontinuous front models

In the design of explosive systems, the generic problem that one must consider is the propagation of a well-developed detonation wave sweeping through an explosive charge with a complex shape. At a given instant of time, the lead detonation shock is a surface that occupies a region of the explosive and has a dimension that is characteristic of the explosive device, typically on the scale of meters. The detonation shock is powered by a detonation reaction zone, sitting immediately behind the shock, which is one the scale of 1 mm or less. Thus, the ratio of the reaction zone thickness to the device dimension is on the order of 1/1000 or less. This scale disparity can lead to great difficulties in computing three-dimensional detonation dynamics. An attack on the dilemma in the computation of detonation systems has led to the invention of subscale models for a propagating detonation front that we refer to herein as program burn models. The program burn model does not resolve the fine scale of the reaction zone; instead the goal is to solve for the hydrodynamics of the inert product gases on a coarse grid scale, which is insufficient to resolve the physical reaction zone. We first show that traditional program burn algorithms for detonation hydrocodes used for explosive design are inconsistent and yield incorrect shock dynamic behavior. To overcome these inconsistencies, we discuss a new class of program burn models based on detonation shock dynamic theory. This new class yields more consistent and robust algorithms that better reflect the correct shock dynamic behavior.