Guided moments formalism: A new efficient full-neutrino treatment for astrophysical simulations

We present the new guided moments (GM) formalism for neutrino modeling in astrophysical scenarios like core-collapse supernovae and neutron star mergers. The truncated moments approximation (M1) and Monte-Carlo (MC) schemes have been proven to be robust and accurate in solving the Boltzmann equation for neutrino transport. However, it is well known that each method exhibits specific strengths and weaknesses in various physical scenarios. The GM formalism effectively solves these problems, providing a comprehensive scheme capable of accurately capturing the optically thick limit through the exact M1 closure and the optically thin limit through an MC-based approach. In addition, the GM method also approximates the neutrino distribution function with a reasonable computational cost, which is crucial for the correct estimation of the different neutrino-fluid interactions. Our work provides a comprehensive discussion of the formulation and application of the GM method, concluding with a thorough comparison across several test problems involving the three schemes (M1, MC, GM) under consideration.