Numerical Analysis of Relativistic Boltzmann-kinetic Equations to Solve Relativistic Shock Layer Problems

TL;DR

This paper numerically analyzes relativistic shock layer problems using two relativistic Boltzmann models, revealing differences in heat flux profiles and behaviors of projected moments in nonequilibrium regions.

Contribution

It compares Marle and Anderson-Witting models for relativistic shock layers, clarifying their differences and behaviors in nonequilibrium conditions.

Findings

Heat flux profiles differ from Navier-Stokes-Fourier law.

Projected moments behaviors are clarified in nonequilibrium regions.

Differences between models are due to relaxational rate dependencies.

Abstract

The relativistic shock layer problem was numerically analyzed by using two relativistic Boltzmann-kinetic equations. One is Marle model, and the other is Anderson-Witting model. As with Marle model, the temperature of the gain term was determined from its relation with the dynamic pressure in the framework of 14-moments theory. From numerical results of the relativistic shock layer problem, behaviors of projected moments in the nonequilibrium region were clarified. Profiles of the heat flux given by Marle model and Anderson-Witting model were quite adverse to the profile of the heat flux approximated by Navier-Stokes-Fourier law. On the other hand, profiles of the heat flux given by Marle model and Anderson-Witting model were similar to the profile approximated by Navier-Stokes-Fourier law. Additionally we discuss the differences between Anderson-Witting model and Marle model by focusing on the fact that the relaxational rate of the distribution function depends on both flow velocity and molecular velocity for Anderson-Witting model, while it depends only on the molecular velocity for Marle model.