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Mie–Grüneisen type equations of state (EOS) are widely used to describe the thermodynamics of solids, liquids, and gases in a variety of physics problems, including shock wave dynamics in condensed materials and the thermodynamic behavior of dense gases generated by detonation waves. The Jones–Wilkins–Lee (JWL), Cochran–Chan, and original Mie–Grüneisen EOSs are relevant examples. However, these EOSs present several major difficulties. First, their range of validity is limited because these EOSs are fitted to a reference curve and tolerate only small deviations from that curve. The second difficulty lies in the complexity of the mathematical formulations, affecting the efficiency of pressure relaxation solvers. These two difficulties give rise to a third. Under extreme flow conditions, computational failures are quite common. Methods for "extending" the equations of state are often used to continue the computations. For example, below a certain arbitrary density, the JWL EOS is sometimes extended to the ideal-gas EOS. A fundamentally new method is presented in this work. It consists of using the much simpler Noble–Abel-stiffened-gas EOS as a predictor, to close the corresponding flow model. A thermodynamic relaxation step follows the prediction step. The solution is projected onto the target EOS, in this case the Mie–Grüneisen EOS, with the help of additional transport equations. Therefore, the flow model is an extended version, much more efficient for numerical resolution. This method solves the three problems above by extending the validity domain of the thermodynamic formulation, making the relaxation solvers much faster, and dramatically increasing the robustness of computations. [ABSTRACT FROM AUTHOR]

The Noble–Abel (NA) equation of state (EOS) is widely used in the interior ballistics of guns as well as rocket propulsion computations. Its simplicity and accuracy are key points for intensive computations with hyperbolic two-phase flow models considered in interior ballistics codes. An alternative formulation is examined in the present contribution through a first-order virial (VO1) equation of state. Appropriate methods for the determination of related parameters, such as specific gas constant, co-volume, and condensed material energy, for both formulations (NA and VO1) are presented. For this, a combination of closed bomb vessel experiments and thermochemical code computations is needed. An extended VO1 EOS with temperature-dependent specific heat is examined. Then, its extension to multiple reactive materials is addressed. Examples are examined for each formulation (NA and VO1) and comparisons are done with the Becker–Kistiakowsky–Wilson (BKW) EOS as reference. Several conclusions have emerged. First, a consideration of the specific heat temperature dependance in computations of the interior ballistics of guns appeared insignificant. Second, VO1 appeared to be more accurate than NA, particularly when gas density is beyond the range used for EOS parameter determination. Last, regarding mixtures of condensed reactive materials, producing burnt gas mixtures, NA again appeared to be less accurate than VO1. However, its formulation is explicit, while VO1 requires numerical solving of a non-linear equation, with consequences on computational cost. [ABSTRACT FROM AUTHOR]