We report the performance of a newly implemented fourth-order accurate finite-volume Harten-Lax-van Leer-contact Riemann solver in the adaptive-mesh-refinement numerical relativity code sacra-mpi. First, we validate our implementation in one-dimensional special relativistic hydrodynamics tests, i.e., a simple wave and shock tube test, which have analytic solutions. We demonstrate that the fourth-order convergence is achieved for the smooth flow, which cannot be achieved in our original second-order accurate finite-volume Riemann solver. We also show that our new solver is robust for the strong shock wave emergence problem. Second, we validate the implementation in a dynamical spacetime by demonstrating that sacra-mpi perfectly preserves the $\pi$ symmetry without imposing the $\pi$ symmetry in a short-term ($\sim 20\mathrm{ms}$ in the inspiral and subsequent postmerger phase) nonspinning equal-mass binary neutron star merger simulations. Finally, we quantify the accuracy of $\approx 28$ cycle inspiral gravitational waveforms from binary neutron star mergers by conducting a resolution study with $\approx 78$, 94, 118, and 135 m. We find that the fourth-order accurate Riemann solver achieves the convergence order $\approx 2.1\pm 0.05–2.4\pm 0.27$, i.e., slightly evolving with time, in the inspiral gravitational wave phase, while the second-order accurate Riemann solver achieves the convergence order $\approx 2.0\pm 0.5$. The residual phase error towards the continuum limit at the merger is $0.27\pm 0.07\mathrm{rad}$ and $0.58\pm 0.22\mathrm{rad}$ out of a total phase of $\approx 176\mathrm{rad}$, respectively, for the fourth- and second-order accurate Riemann solver.

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• Fluids & classical fields in curved spacetime
• General relativity
• Gravitational wave sources
• Gravitational waves
• Nuclear physics of explosive environments