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Numerical relativity simulations are the only way to calculate exactgravitational waveforms from binary neutron star mergers and to designtemplates for gravitational-wave astronomy. The accuracy of these numericalcalculations is critical in quantifying tidal effects near merger that arecurrently one of the main sources of uncertainty in merger waveforms. In thiswork, we explore the use of an entropy-based flux-limiting scheme forhigh-order, convergent simulations of neutron star spacetimes. The schemeeffectively tracks the stellar surface and physical shocks using the residualof the entropy equation thus allowing the use of unlimited central flux schemesin regions of smooth flow. We perform the first neutron star merger simulationswith such a method and demonstrate up to fourth-order convergence in thegravitational waveform phase. The scheme reduces the phase error up to a factorfive when compared to state-of-the-art high-order characteristic schemes andcan be employed for producing faithful tidal waveforms for gravitational-wavemodelling.

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