Numerical comparison of Riemann solvers for astrophysical hydrodynamics

TL;DR

This paper compares a new entropy-stable Riemann solver with existing algorithms in astrophysical hydrodynamics, demonstrating its efficiency and comparable accuracy through various tests.

Contribution

It introduces and evaluates a new positive, entropy-stable Riemann solver integrated into an astrophysical code, comparing its performance with established methods.

Findings

The new solver is faster without significant accuracy loss.

Subtle differences observed in shock tube and turbulence tests.

The solver performs well in 2D and 3D simulations.

Abstract

The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.