A review of macrokinetic models and equations for heterogeneous explosives

This paper presents a comprehensive review of models and equations describing the macrokinetics of heterogeneous explosive reactions, most of which have been developed over the past two decades. Applications of these models to detonation simulations under various loading conditions and for a wide range of explosive formulations are also discussed. The review begins with an overview of shock-to-detonation transition modeling, including the mechanisms responsible for microscale hot-spot formation. The Forest Fire model is examined in detail, with emphasis on calibration methodologies derived from detonation development tests that have influenced subsequent model formulations. Widely used approaches are then discussed, including the Ignition and Growth (I&G) model, intermediate-phase models such as the Tang–Johnson–Forest (TJF) model, hybrid formulations, the History Variable Reactive Burn (HVRB) model, the entropy-based CREST model, the Arrhenius–Wescott–Stewart–Davis (AWSD) model, multiscale approaches (SURF, Kim, DZK, CHARM, and JZ models), and the Statistical Hot Spot (SHS) model. For each model, the underlying assumptions, calibration methodologies, and coupling with hydrodynamic equations are discussed. Representative applications are presented to highlight both the predictive capabilities and the limitations of these formulations.