| Numerical simulations that solve the full set of the Einstein field equations and general relativistic hydrodynamic equations are central to the understanding of the astrophysics processes involving neutron stars and black holes, which are crucial to gravitational wave astronomy and high-energy astronomy. The dissertation reports on the progress made in the construction of a numerical code, GR-Astro, which enables such simulations, and its applications to the neutron star inspiral coalescences.; An important; extension of GR-Astro, namely, GR-Astro-AMR that makes possible adaptive mesh refinement (AMR) simulations is described. Diagnostic tools for analyzing the properties of the spacetime constructed numerically with the AMR infrastructure are built. With these tools, the accuracy of the AMR simulations is compared with results obtained by other research groups on the neutron star inspiral problem. The behavior of different hydrodynamic treatments in used with the AMR. simulations is studied. The importation of binary neutron star initial data obtained in a spectral method code into GR-Astro-AMR for used in AMR numerical evolutions is enabled in this work.; Making use of the developments described above, we demonstrated that a neutron star binary starting with the conformally flat quasi-equilibrium irrotational initial data will have the central density of the stars decreases as the separation of the stars decreases, disproving the "premature collapse conjecture" of Wilson et al. |
