Numerical analysis of relativistic shock layer problem by using relativistic Boltzmann–kinetic equations

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 and Anderson–Witting models were similar to the profile approximated by Navier–Stokes–Fourier law. On the other hand, profiles of the dynamic pressure given by Marle and Anderson–Witting models were quite opposite to the profile of the dynamic pressure 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.