Numerical Methods for Simulating Core-collapse Supernovae

Massive stars can end their lives in spectacular explosions known as supernovae. Since the interior of a star cannot be directly observed, computer simulations are required to investigate the interplay between the numerous processes that power the explosion. In this thesis, we investigate the effect of material falling back after the explosion on the properties of the nascent black hole or neutron star. We also develop a new method for modelling neutrino radiation, which, we believe, will provide the foundation for upcoming explosion modelling studies.