Characteristic Decomposition for Relativistic Numerical Simulations: I. Hydrodynamics

TL;DR

This paper introduces a new method for deriving characteristic decompositions in relativistic hydrodynamics using quasi-invertible transformations, simplifying the process and enabling more accurate numerical simulations.

Contribution

It presents a novel transformation-based approach to obtain characteristic decompositions, including for nuclear statistical equilibrium, simplifying previous methods.

Findings

Recovered known relativistic hydrodynamics decomposition more simply

Introduced characteristic decomposition for nuclear statistical equilibrium

Laid groundwork for GRMHD decomposition in Paper II

Abstract

The characteristic decomposition for GRMHD is not known in a form useful for current numerical simulations. This prevents us from using the most accurate known computational methods, such as full-wave Riemann solvers. In this paper, we present a new method of finding decompositions. The method is based on transformations from the comoving frame, where the fluid flow is simplest and the decomposition has been known for a long time. The key innovation we introduce is that of quasi-invertible transformations. In this first paper, we introduce these transformations using the simpler example of relativistic hydrodynamics. We recover the known decomposition for relativistic hydrodynamics in somewhat simpler form than previously derived, and without the need for computer algebra. A new result in this paper is the characteristic decomposition when the the evolution tracks the composition of a fluid in nuclear statistical equilibrium. In Paper II of this series, we apply a quasi-invertible transformation to derive the complete characteristic decomposition for GRMHD in the conserved variables used in simulations.