Compact representation of the generic five-equation model with additional temperature-equilibrium

This paper presents a compact formulation of the generic five-equation (GFE) model for compressible multimaterial flows under additional temperature-equilibrium. By analyzing the pressure- and temperature-equilibrium closure used in its equivalent model (i.e., four-equation model), a novel method for deriving the distribution coefficient (DC) that governs the evolution of volume fractions in the GFE model is presented. Subsequently, through the introduction of three commonly used thermodynamic derivatives (i.e., the coefficient of thermal expansion, the isothermal compressibility, and the specific heat at constant pressure), we ultimately obtain the formula of DC in the GFE model with additional temperature-equilibrium that is not only simple but also highly compact in form. Numerical verifications confirm the correctness of the derivation.