Empirical Correlations Between the Function of Entropy (Z_s) and Net Artificial Viscous Work in a Shock Physics Hydrocode

Concerning reactive burn models that are used to model shock-induced reactions, the CREST model is unique in that it uses entropy as a reaction potential. Entropy is a thermodynamic state variable, and it is solved from the equation of state (EOS). However, it is susceptible to numerical errors, especially for Eulerian hydrocodes during the mass advection and remap steps. During a renewed effort to implement the CREST model into the shock physics hydrocode CTH, several methods were explored to reduce the numerical errors in the function of entropy, i.e., Z_S. Empirical correlations were found between the function of entropy and the net artificial viscous work during the passage of a shock wave. Here, these empirical correlations are discussed with respect to mesh convergence and the EOS parameters. Additionally, results are shown for 46 different EOSs, consisting of metals and metal alloys, polymers, and unreacted energetic materials. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties to a physical law (e.g., the fourth-power law of Grady [1]).

^[1]Grady, D.E., “Structured shock waves and the fourth-power law,” J. Appl. Phys., 107(1):013506, 2010.