An analytic and complete equation of state for detonation products

Hydrodynamic simulations of high explosives require an equation of state (EOS) to model the thermodynamics of the detonation products. When solving large-scale multi-physics problems, it is desirable to have computationally-efficient models in analytic form that ensure well-defined derivative properties such as sound speed. The latest advances in first-principles molecular dynamics provide thermodynamic surfaces in a wide range of phase space; thus, there is a need for analytic models capable of capturing off-nominal regions. This work introduces a complete and thermodynamically consistent EOS that remains thermodynamically stable and convex for all positive specific volume and temperature. The model is constructed using the Helmholtz free energy where the specific heat and Grüneisen parameter are functions of both temperature and specific volume. To ensure computational efficiency, the functional forms are analytically invertible in pressure, temperature, and specific internal energy. First-principles reactive Monte Carlo simulations of pentaerythritol tetranitrate (PETN) products using density functional theory are used to calibrate the EOS parameters and highlight the main model properties.