Implementation of advanced Riemann solvers in a neutrino-radiation magnetohydrodynamics code in numerical relativity and its application to a binary neutron star merger

TL;DR

This paper introduces advanced Riemann solvers and a constrained transport scheme into a neutrino-radiation magnetohydrodynamics code, improving accuracy in simulations of binary neutron star mergers in numerical relativity.

Contribution

The implementation of HLLC and HLLD Riemann solvers with an advanced constrained transport scheme in a numerical relativity code is novel and enhances simulation accuracy.

Findings

Advanced solvers yield more accurate results than HLLE.

Simulations with advanced solvers show longer neutron star lifetimes.

Magnetorotational instability is less resolved with HLLE, affecting magnetic field evolution.

Abstract

We implement advanced Riemann solvers HLLC and HLLD \cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transport scheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiation magnetohydrodynamics code. We validate our implementation by performing a series of one- and multi-dimensional test problems for relativistic hydrodynamics and magnetohydrodynamics in both Minkowski spacetime and a static black hole spacetime. We find that the numerical solutions with the advanced Riemann solvers are more accurate than those with the HLLE solver \cite{DelZanna:2002rv}, which was originally implemented in our code. As an application to numerical relativity, we simulate an asymmetric binary neutron star merger leading to a short-lived massive neutron star both with and without magnetic fields. We find that the lifetime of the rotating massive neutron star formed after the merger and also the amount of the tidally-driven dynamical ejecta are overestimated when we employ the diffusive HLLE solver. We also find that the magnetorotational instability is less resolved when we employ the HLLE solver because of the solver's large numerical diffusivity. This causes a spurious enhancement both of magnetic winding resulting from large scale poloidal magnetic fields, and also of the energy of the outflow induced by magnetic pressure.