Relativistic Rational Extended Thermodynamics of Polyatomic Gases with a New Hierarchy of Moments

TL;DR

This paper develops a relativistic extended thermodynamics framework for polyatomic gases using a new hierarchy of moments, deriving the associated equations, analyzing limits, and exploring applications in cosmology.

Contribution

It introduces a novel hierarchy of moments for relativistic polyatomic gases, derives the moment equations, and establishes the system's well-posedness and hyperbolicity.

Findings

The system is symmetric hyperbolic near equilibrium.

The ultra-relativistic and classical limits are characterized.

A simplified 6-moment subsystem models bulk viscosity effects.

Abstract

A relativistic version of the rational extended thermodynamics of polyatomic gases based on a new hierarchy of moments that takes into account the total energy composed by the rest energy and the energy of the molecular internal mode is proposed. The moment equations associated with the Boltzmann-Chernikov equation are derived, and the system for the first $15$ equations is closed by the procedure of the maximum entropy principle and by using an appropriate BGK model for the collisional term. The entropy principle with a convex entropy density is proved in a neighborhood of equilibrium state, and, as a consequence, the system is symmetric hyperbolic and the Cauchy problem is well-posed. The ultra-relativistic and classical limits are also studied. The theories with $14$ and $6$ moments are deduced as principal subsystems. Particularly interesting is the subsystem with $6$ fields in which the dissipation is only due to the dynamical pressure. This simplified model can be very useful when bulk viscosity is dominant and might be important in cosmological problems. Using the Maxwellian iteration, we obtain the parabolic limit, and the heat conductivity, shear viscosity, and bulk viscosity are deduced and plotted.