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

We implement advanced Riemann solvers HLLC and HLLD\cite{Mignone:2005ft,MUB:2009} together with an advanced constrained transportscheme \cite{Gardiner:2007nc} in a numerical-relativity neutrino-radiationmagnetohydrodynamics code. We validate our implementation by performing aseries of one- and multi-dimensional test problems for relativistichydrodynamics and magnetohydrodynamics in both Minkowski spacetime and a staticblack hole spacetime. We find that the numerical solutions with the advancedRiemann solvers are more accurate than those with the HLLE solver\cite{DelZanna:2002rv}, which was originally implemented in our code. As anapplication to numerical relativity, we simulate an asymmetric binary neutronstar merger leading to a short-lived massive neutron star both with and withoutmagnetic fields. We find that the lifetime of the rotating massive neutron starformed after the merger and also the amount of the tidally-driven dynamicalejecta are overestimated when we employ the diffusive HLLE solver. We also findthat the magnetorotational instability is less resolved when we employ the HLLEsolver because of the solver's large numerical diffusivity. This causes aspurious enhancement both of magnetic winding resulting from large scalepoloidal magnetic fields, and also of the energy of the outflow induced bymagnetic pressure.