Evaluating Accuracy in Binary Neutron Star Merger Simulations: Comparative Analysis of Five Computational Codes

Gravitational waves from binary neutron star (BNS) mergers are crucial for probing matter under extreme conditions. Due to timited observational data, we rely on numerical relativity simulations. Simulating BNS mergers remains challenging, particularly in ensuring the reliability and convergence of codes, especially in post-merger. In this study, we systematically evaluate open-source gravitational wave data from five prominent BNS merger simulation codes. After outlining advances and challenges in BNS simulations, we describe the role of quasi-universal relations, which quantify the impact of the neutron star's equation of state on gravitational wave signals. We introduce a novel method to assess code convergence under oscillatory behaviors, often present in computational fluid dynamics. Our results include comparative analyses of tidal deformability, convergence behavior, and predictions of quasi-universal relations across hundreds of simulated waveforms. By benchmarking these codes against existing analytical relations and new fits, our work aims to improve simulation reliability and advance gravitational wave template accuracy