Gravitational waveforms from binary neutron star mergers with high-order WENO schemes in numerical relativity

The theoretical modeling of gravitational waveforms from binary neutron star mergers requires precise numerical relativity simulations. Assessing convergence of the numerical data and building the error budget is currently challenging due to the low accuracy of general-relativistic hydrodynamics schemes and to the grid resolutions that can be employed in $(3+1)$-dimensional simulations. In this work, we explore the use of high-order weighted-essentially-nonoscillatory (WENO) schemes in neutron star merger simulations and investigate the accuracy of the waveforms obtained with such methods. We find that high-order WENO schemes can be robustly employed for simulating the inspiral-merger phase and they significantly improve the assessment of the waveform's error budget with respect to finite-volume methods. High-order WENO schemes can be thus efficiently used for high-quality waveforms production, also in future large-scale investigations of the binary parameter space.