Relaxation method for detonations in condensed explosives with pressure–temperature-equilibrium models and Mie–Grüneisen type equations of state
Résumé
This paper deals with detonation waves in condensed explosives in the context of pressure and temperature equilibrium models. Most engineering solvers for detonation waves in condensed explosives are based on the reactive Euler equations, which model flows evolving in both temperature and pressure equilibrium conditions. Although the assumption of thermal equilibrium is physically questionable, the reactive Euler equations remain the most popular model because of its convenience. Conventional methods rely on Mie–Grüneisen equations of state (EOS) and are challenged by their limited applicability, high computational complexity, and frequent failure. A previous publication addressed these issues by using the Noble–Abel-stiffened-gas EOS as a predictor, followed by a relaxation step to map the solution to the physical target EOS. This novel thermodynamic relaxation framework was originally introduced in the context of mechanical equilibrium. The present work builds on this novel method to encompass both mechanical and thermal equilibrium, thus enabling the treatment of detonation waves in condensed explosives within the framework of pressure and temperature equilibrium models. The proposed method is capable of treating both interfacial flows through “diffuse interface” formulations, and mixture flows in mechanical and thermal equilibrium. In addition, the proposed method demonstrates improved computational robustness, a significant increase in efficiency, and greater flexibility.
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