Core-Collapse Supernova Simulations With Spectral Two-Moment Neutrino Transport

The primary focus of this dissertation is to develop a next-generation, state-of-the-art neutrino kinetics capability that will be used in the context of the next-generation, state-of-the-art core-collapse supernova (CCSN) simulation frameworks \thornado\ and \FLASH.\index{CCSN} \thornado\ is a \textbf{t}oolkit for \textbf{h}igh-\textbf{or}der \textbf{n}eutrino-r\textbf{ad}iation hydr\textbf{o}dynamics, which is a collection of modules that can be incorporated into a simulation code/framework, such as \FLASH, together with a nuclear equation of state (EOS)\index{EOS} library, such as the \WeakLib\ EOS tables. The first part of this work extends the \WeakLib\ code to compute neutrino interaction rates from~\cite{Bruenn_1985} and produce corresponding opacity tables.\index{Bruenn 1985} The processes of emission, absorption, scattering of neutrinos from nucleons and nuclei, neutrino--electron scattering, and neutrino pair production and annihilation are included. The second part of this dissertation builds the special-relativity-corrected (\Ov) neutrino radiation module in \thornado, based on the spectral two-moment method.\index{\Ov} This part of the work involved studying the accuracy, efficiency, and robustness of the numerical solver. We propose a special kind of implicit-explicit scheme, PDARSs, based on efficiency, diffusion accuracy, and physics-preserving (positivity-preserving and realizability-preserving) requirements. \index{PD-ARS} Emission, absorption, scattering of neutrinos from nucleons and nuclei, neutrino--electron scattering, and neutrino pair production and annihilation are included as neutrino--matter couplings. The third part of this work builds interfaces between \FLASH\ and \thornado, \FLASH\ and \WeakLib, and \thornado\ and \WeakLib\ for simulations with the \FLASH\ hydrodynamics module, \WeakLib\ EOS module, and \thornado\ neutrino kinetics module. This part of the work includes data mapping between finite-volume grids and finite-element grids, time-step balancing between hydrodynamics time steps and radiation transport time steps, and GPU enhancement. The fourth part of this work makes a detailed comparison of the results of a spherically symmetric simulation performed by \FLASH+\thornado\ with the result of the \chimera\ code, which is a sophisticated, mature, and evolving code with spectral flux-limited diffusion (one-moment) neutrino kinetics and improved input physics~\citep{bruenn_etal_2020}. This part of the work demonstrates the ability of \FLASH+\thornado\ to perform CCSN simulations and quantifies the potential differences between the two codes caused by the different neutrino kinetics treatments, as well as other differences. Supported by all of the above work, spherically symmetric CCSN simulations with spectral two-moment neutrino kinetics were performed for three low-mass progenitors of 9-, 10-, and 11-Solar-mass (\solarmass) from~\cite{sukhbold_etal_2016}