An improved exact Riemann solver for multi-dimensional relativistic flows

Abstract

We extend our approach for the exact solution of the Riemann problem in relativistic hydrodynamics to the case in which the fluid velocity has components tangential to the initial discontinuity. As in one-dimensional flows, we show here that the wave pattern produced in a Riemann problem with multi-dimensional relativistic flows can be predicted entirely by examining the initial conditions. Our method is logically very simple and allows for a numerical implementation of an exact Riemann solver which is both straightforward and computationally efficient. The simplicity of the approach is also important for revealing special relativistic effects responsible for a smooth transition from one wave pattern to another when the tangential velocities in the initial states are suitably varied. Although this paper is focused on a flat space–time, the local Lorentz invariance allows its use also in fully general relativistic calculations.