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

Understand

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.