Coupled constitutive relations for two-temperature model for polyatomic gases: Linear analysis, light scattering, and shock propagation

Abstract

This article presents a new two-temperature coupled constitutive relations (CCR) model for polyatomic gases, developed using CCR based on classical irreversible thermodynamics. The model includes nonlinear terms in entropy and heat flux to better capture non-equilibrium phenomena. It offers a significant improvement over the one-temperature CCR model recently introduced by Rana and Barve [“A second-order constitutive theory for polyatomic gases: Theory and applications,” J. Fluid Mech. 958, A23 (2023)] and simplifies the complex behavior of polyatomic gases, providing a practical alternative to the Boltzmann equation or molecular dynamics simulations. The proposed model accurately describes steady-state shocks and Rayleigh–Brillouin light scattering, showing particular advantages in rarefied flow scenarios. Additionally, the model exhibits strong stability and consistency in capturing non-equilibrium processes, making it suitable for a wide range of flow conditions.