Astrophysical fluid dynamical problems rely on efficient numerical solution techniques for hyperbolic and parabolic terms. Efficient techniques are a

A reactive flow model for the tri-amino-tri-nitro-benzene (TATB) based plastic bonded explosive PBX 9502 (95% TATB, 5% polymeric binder Kel-F 800) is presented. This newly devised model is based primarily on the shock temperature of the material, along with local pressure, and accurately models a broader range of detonation and initiation scenarios. Specifically, sensitivity changes to the initial explosive temperature are accounted for naturally and with a single set of parameters. The equation of state forms for the reactants and products, as well as the thermodynamic closure of pressure and temperature equilibration, are carried over from the Wescott-Stewart-Davis (WSD) model [Wescott et al., J. Appl. Phys. 98, 053514 (2005) and “Modeling detonation diffraction and dead zones in PBX-9502,” in Proceedings of the Thirteenth International Detonation Symposium (2006)]. This newly devised model, with Arrhenius state dependence on the shock temperature, based on the WSD equation of states, is denoted by AWSD. Modifying an existing implementation of the WSD model to the AWSD model in a hydrocode is a rather straightforward procedure.

The dynamics of a one-dimensional detonation predicted by a one-step irreversible Arrhenius kinetic model are investigated in the presence of mass, momentum and energy diffusion. A study is performed in which the activation energy is varied and the length scales of diffusion and reaction are held constant. As the activation energy is increased, the system goes through a series of period-doubling events and eventually undergoes a transition to chaos. The rate at which these bifurcation points converge is calculated and shown to be in agreement with the Feigenbaum constant. Within the chaotic regime, there exist regions in which there are limit cycles consisting of a small number of oscillatory modes. When an appropriately fine grid is used to capture mass, momentum and energy diffusion, predictions are independent of the differencing scheme. Diffusion affects the behaviour of the system by delaying the onset of instability and strongly influencing the dynamics in the unstable regime. The use of the reactive Euler equations to predict detonation dynamics in the unstable and marginally stable regimes is called into question as the selected reactive and diffusive length scales are representative of real physical systems; reactive Navier–Stokes is a more appropriate model in such regimes.