A practical guide to a moment approach for neutrino transport in numerical relativity

The development of a neutrino moment based radiative-transfer code to simulate binary neutron-star mergers can easily become an obstacle path because of the numerous ways in which the solution of the equations may fail. We describe the implementation of the grey M1 scheme in our fully general-relativistic magnetohydrodynamics code and detail those choices and strategies that could lead either to a robust scheme or to a series of failures. In addition, we present new tests designed to show the consistency and accuracy of our code in conditions that are similar to realistic merging conditions and introduce a new, publicly available, benchmark based on the head-on collision of two neutron stars. This test, which is computationally less expensive than a complete merging binary but has all the potential pitfalls of the full scenario, can be used to compare future implementations of M1 schemes with the one presented here.