Comparison of Viscosities from the Chapman-Enskog and Relaxation Time Methods

TL;DR

This paper compares shear viscosity calculations from Chapman-Enskog and relaxation time methods across various gas models, revealing that agreement depends heavily on the energy dependence of differential cross sections.

Contribution

It provides a detailed quantitative comparison of viscosity results from two methods for different gas models with specific cross sections.

Findings

Agreement varies with energy dependence of cross sections

Relativistic effects influence viscosity calculations

Method discrepancies are model-dependent

Abstract

A quantitative comparison between the results of shear viscosities from the Chapman-Enskog and relaxation time methods is performed for selected test cases with specified elastic differential cross sections: (i) the non-relativistic, relativistic and ultra-relativistic hard sphere gas with angle and energy independent differential cross section, (ii) the Maxwell gas, (iii) chiral pions and (iv) massive pions. Our quantitative results reveal that the extent of agreement (or disagreement) depends very sensitively on the energy dependence of the differential cross sections employed.