Characteristic Decomposition for Relativistic Numerical Simulations: II. Magnetohydrodynamics

TL;DR

This paper derives the characteristic decomposition for relativistic magnetohydrodynamics in the coordinate frame used in numerical simulations, enabling more accurate computational methods like full-wave Riemann solvers.

Contribution

It applies a quasi-invertible transformation method to derive the characteristic decomposition in the simulation's coordinate frame, simplifying previous complex formulations.

Findings

Derived the characteristic decomposition in the coordinate frame used in simulations.

Enabled the use of full-wave Riemann solvers for GRMHD.

Simplified the mathematical form of the decomposition.

Abstract

The characteristic decomposition for GRMHD in the comoving frame of the fluid has been known for a long time. However, it has not been known in the coordinate frame of the simulation and in terms of the conserved variables evolved in typical numerical simulations. This paper applies the method of quasi-invertible transformations developed in Paper I to derive this decomposition. Among other benefits, this will allow us to use the most accurate known computational methods, such as full-wave Riemann solvers. The results turn out to be simpler than expected based on earlier attempts.