Low-parametric equations of state for polycrystalline bodies used in CFD applications

We developed a method for constructing low-parametric equations of state (EOS) for polycrystalline substances in the compression region. The method was applied to silicon dioxide ($SiO_2$). This compound is one of the main rock-forming materials in the Earth's crust and mantle, and also occurs on other planets. Knowledge of its EOS at high pressures is essential for studying the formation and evolution of celestial bodies and for predicting the effects of their collisions.
In shock-wave research, silicon dioxide serves as a reference material in experiments based on the reflection method. The validity of this method depends on the availability of a wide-range EOS for the reference material. Because $SiO_2$ exhibits pronounced polymorphism, its polymorphic transitions must be taken into account when determining its EOS.
Equations of state for the individual polymorphs were obtained from thermodynamically consistent relations derived from power-law potentials. A pre-calculated phase diagram provided the basis for the numerical implementation of the polymorphic EOS. A procedure was developed to calculate the shock adiabat with allowance for polymorphism, and the results were compared with data from shock-wave experiments.