An Improved Exact Riemann Solver for Multidimensional Relativistic Flows

TL;DR

This paper presents an efficient, exact Riemann solver for multidimensional relativistic hydrodynamics that accounts for tangential velocities, enabling accurate wave-pattern predictions and revealing relativistic effects in fluid flows.

Contribution

It extends the exact Riemann solver to multidimensional flows with tangential velocities, simplifying implementation and enhancing understanding of relativistic wave patterns.

Findings

Wave-patterns can be predicted from initial conditions.

The solver is computationally efficient and straightforward.

Relativistic effects cause smooth transitions between wave-patterns.

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 here show that the wave-pattern produced in a multidimensional relativistic Riemann problem 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. While the content of this paper is focussed on a flat spacetime, the local Lorentz invariance allows its use also in fully general relativistic calculations.