A DG-IMEX method for two-moment neutrino transport: Nonlinear solvers for neutrino-matter coupling

TL;DR

This paper develops and compares nonlinear solvers for implicit neutrino-matter coupling in core-collapse supernova simulations, demonstrating that a nested Anderson-accelerated fixed-point method is most efficient.

Contribution

It introduces and evaluates two formulations and four iterative solvers for nonlinear systems in neutrino transport, highlighting the superior performance of a nested Anderson-accelerated fixed-point approach.

Findings

Nested Anderson-accelerated fixed-point solver outperforms others in efficiency.

The methods are tested on realistic supernova matter profiles.

The approach improves the implicit treatment of neutrino-matter interactions.

Abstract

Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn~85 opacity set. The implicit systems arise from the discretization of a non-relativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems -- a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixed-point iteration and Newton's method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.