Preparing Binary Neutron Star Simulations for Precision Gravitational Wave Astronomy

Next-generation gravitational wave (GW) detectors demand precise and reliable binary neutron star (BNS) simulations. Meeting this requirement calls for rigorous modeling of GW systematics, quantification of numerical errors, and validation of numerical relativity (NR) codes to achieve the needed precision. Convergence analysis is essential for evaluating how well NR codes resolve the physics of BNS mergers, yet standardization remains difficult due to variations in numerical methods and physical assumptions. We implement techniques adapted from computational fluid dynamics to streamline convergence calculations, estimate numerical error, and apply correction factors when the solution approaches the asymptotic regime, thereby enhancing the robustness of the results. This framework is applied to open GW data from multiple leading NR codes to assess convergence behavior across physical parameters. Our results outline a path toward standardized verification and improved numerical accuracy in BNS simulations, preparing NR codes for the precision demands of next-generation GW observations.