In this thesis, we present simulations of merging binary neutron stars, carried out using the publicly available FLASH code framework. These are 3D Newtonian magnetohydrodynamic simulations, in which we have included gravitational wave effects through the use of a source term. We trial different implementations of this source term and discuss the results. We then use this model to investigate the role of magnetic fields in binary neutron star mergers. We endow each neutron star with a dipolar magnetic field and examine how the orientation of the dipole affects the strength and structure of the magnetic field during the merger. This has important implications for the ability of the merger remnant to produce a short gamma ray burst jet.
In a second project, we simulate a magnetized accretion torus surrounding a black hole. We implement a model black hole in the FLASH code framework using a Pseudo-Newtonian potential to reproduce features, such as the innermost stable circular orbit, which are important to accretion disc studies. We compare the results of our magnetized accretion disc simulations with similar studies, finding broad agreement with accretion rates and the general structure of the magnetic field
