General relativistic neutrino transport with spectral methods

Abstract

Supernovae numerical simulations are highly demanding in computational power, yet they are also rapidly increasing in complexity. There is now a very high demand in new methods for neutrino treatment, due to the fact that neutrino is at the same time a crucial ingredient and the most expensive one in computational resources. A possibility to explore is the treatment by spectral methods, because they are known to require less resources. It is the purpose of a new code, named Lorene's Ghost (for Lorene's gravitational handling of spectral transport), developed to treat the problem of neutrino transport in supernovae. The code can handle full phase-space dependent problems (6D + time), retains the full energy dependence of the neutrinos, and can also handle general relativity in the conformally flat approximation. Several points of the formalism needed to obtain a formulation of the general relativistic Boltzmann equation adapted to our case are discussed, as well as some technical aspects of spectral methods.