On the relative importance of second-order terms in relativistic dissipative fluid dynamics

TL;DR

This paper evaluates the significance of second-order inverse Reynolds number terms in relativistic dissipative fluid dynamics, derived from the Boltzmann equation, and compares their impact to other second-order terms for a massless Boltzmann gas.

Contribution

It explicitly computes second-order inverse Reynolds number terms and assesses their importance relative to other second-order contributions in relativistic fluid dynamics.

Findings

Second-order inverse Reynolds terms are significant in certain regimes.

Terms of second order in Knudsen number are non-hyperbolic and must be neglected.

The relative importance of these terms depends on the specific physical conditions.

Abstract

In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scattering cross section. Consequently, we assess their relative importance in comparison to the terms which are of the order of the product of Knudsen and inverse Reynolds numbers.