From hyperbolic regularization to exact hydrodynamics for linearized Grad's equations

TL;DR

This paper presents a method to derive hyperbolic, stable linear hydrodynamic equations with arbitrary accuracy in Knudsen number, based on a dynamic invariance principle applied to Grad's thirteen moment system.

Contribution

It introduces a systematic approach to obtain exact, hyperbolic hydrodynamic equations from kinetic models using a dynamic invariance principle.

Findings

Derived exact constitutive relations for stress and heat flux.

Achieved hyperbolic and stable hydrodynamic equations.

Applicable to Grad's thirteen moment system.

Abstract

Inspired by a recent hyperbolic regularization of Burnett's hydrodynamic equations [A. Bobylev, J. Stat. Phys. 124, 371 (2006)], we introduce a method to derive hyperbolic equations of linear hydrodynamics to any desired accuracy in Knudsen number. The approach is based on a dynamic invariance principle which derives exact constitutive relations for the stress tensor and heat flux, and a transformation which renders the exact equations of hydrodynamics hyperbolic and stable. The method is described in detail for a simple kinetic model - a thirteen moment Grad system.