Regularized Gaussian 11-moment equations for polyatomic gases: Derivation, linear analysis, and its applications

This article presents a macroscopic closure for rarefied polyatomic gas flows, focusing on a regularized Gaussian 11-moment (RG11) system. Our model uses a generalized Gaussian distribution-a product of Gaussian and Gamma functions-to capture both translational and internal energies of polyatomic molecules. The closure is achieved through a regularization technique, following Struchtrup & Torrilhon (Physics of Fluids, vol. 15, 2003) approach for R13 equations in monatomic gases. In addition, we use a Bhatnagar-Gross-Krook (BGK)-type relaxation model to evaluate the production terms in the moment equations. The proposed model incorporates three relaxation parameters, which can be tuned to match viscosity, bulk viscosity, and thermal conductivity accurately for the gas under consideration. By applying a Chapman-Enskog-like expansion and an order-of-magnitude analysis, we derive the RG11 equations, featuring non-zero constitutive relations for both internal and translational heat flux. This new formulation is linearly stable in one-dimensional case across all wavelengths and frequencies, aligns well with experimental data for sound wave propagation, and agrees with validated hydrodynamic theories that are known to match experimental results for Rayleigh-Brillouin scattering (RBS), outperforming the Navier-Stokes-Fourier (NSF) equations.