With advance of supercomputers we can now afford simulations with very large
range of scales. In astrophysical applications, e.g. simulating Solar, stellar
and planetary atmospheres, physical quantities, like gas pressure, density,
temperature and plasma $\beta $ can vary by orders of magnitude. This requires a
robust solver, which can deal with a very wide range of conditions and be able
to maintain hydrostatic equilibrium. We reformulate a Godunov-type HLLD Riemann
solver so it would be suitable to maintain hydrostatic equilibrium in
atmospheric applications and would be able to handle low and high Mach numbers,
regimes where kinetic and magnetic energies dominate over thermal energy
without any ad-hoc corrections. We change the solver to use entropy instead of
total energy as the 'energy' variable in the system of MHD equations. The
entropy is *not conserved*, it increases when kinetic and magnetic energy is
converted to heat, as it should. We conduct a series of standard tests with
varying conditions and show that the new formulation for the Godunot type
Riemann solver works and is very promising.

PREPRINT

# DISPATCH methods: an approximate, entropy-based Riemann solver for ideal magnetohydrodynamics

Andrius Popovas

Submitted on 4 November 2022

## Abstract

## Preprint

Comment: 12 pages, 14 figures, submitted to A&A

Subjects: Astrophysics - Instrumentation and Methods for Astrophysics; Astrophysics - Solar and Stellar Astrophysics; Physics - Computational Physics