A Numerical Study of Relativistic Oblique Shock Reflection

TL;DR

This paper investigates relativistic shock reflection in two dimensions using numerical simulations and analytic comparisons, revealing the transition conditions between different shock reflection regimes and analyzing flow properties across relativistic and Newtonian limits.

Contribution

It provides a comprehensive 2D numerical study of relativistic shock reflection, including the transition between regular and Mach reflection, with detailed analytic and simulation comparisons.

Findings

Good agreement between simulations and analytic solutions.

The transition line between RR and MR coincides with the detachment/sonic line.

Flow properties along the sonic line vary between Newtonian and relativistic regimes.

Abstract

Shocks are ubiquitous in astrophysical sources, many of which involve relativistic bulk motions, leading to the formation of relativistic shocks. Such relativistic shocks have so far been studied mainly in one dimension, for simplicity, but the complex nature of the relevant astrophysical flows often requires higher dimensional studies. Here we study the two-dimensional problem of the reflection of a planer shock off of a wall for a general incidence angle and a cold unshocked medium. We use primarily relativistic hydrodynamic numerical simulations, and elaborately compare the results to an analytic treatment. The simulations are performed both in the rest frame S of the unshocked fluid, where the dimensionless proper speed of the singly shocked fluid is $u_1=\Gamma_1\beta_1$ and the shock incidence angle is $\alpha_1$, and in the rest frame S$^\prime$ of the point P of intersection of the incident shock and the wall for regular reflection (RR). Good agreement is obtained between the simulations in these two frames and with the analytic solution. The establishment of a steady flow in frame S$^\prime$ is explored, along with the transition between the strong and weak shock RR solutions. The transition line between RR and Mach reflection (MR) is studied numerically in the $u_1$-$\alpha_1$ plane and found to coincide with the analytic detachment/sonic line. The flow properties along the sonic line are investigated in detail focusing on how they vary between the Newtonian and relativistic limits.