Entropy-limited higher-order central scheme for neutron star merger simulations

Numerical relativity simulations are the only way to calculate exact gravitational waveforms from binary neutron star mergers and to design templates for gravitational-wave astronomy. The accuracy of these numerical calculations is critical in quantifying tidal effects near merger that are currently one of the main sources of uncertainty in merger waveforms. In this work, we explore the use of an entropy-based flux-limiting scheme for high-order, convergent simulations of neutron star spacetimes. The scheme effectively tracks the stellar surface and physical shocks using the residual of the entropy equation thus allowing the use of unlimited central flux schemes in regions of smooth flow. We perform the first neutron star merger simulations with such a method and demonstrate up to fourth-order convergence in the gravitational waveform phase. The scheme reduces the phase error up to a factor five when compared to state-of-the-art high-order characteristic schemes and can be employed for producing faithful tidal waveforms for gravitational-wave modelling.