Supernovae represent powerful sources of gravitational radiation. Their numerical simulation, even of simplified core collapse models, requires numerical techniques that are able to handle strong hydrodynamic shocks and a general-relativistic gravitational field. Such hydrodynamics can be modeled with high-resolution shock-capturing (HRSC) schemes, also known as Godunov schemes, in general relativity, while the Einstein equations for the gravitational field may require much computer power, if solved in the same way. It is there-fore interesting to use spectral methods to model the gravitational field, which is always regular enough to avoid any Gibbs phenomenon, in conjunction with HRSC schemes for the hydrodynamics equations. We present such a code com-bining both methods to model stellar core collapse simulations and the resulting gravitational waves, with the most recent equations of state and a simplified neutrino treatment. Some additional results on neutron star oscillations are also shown.
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