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 nonrelativistic 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 degrees 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.

中微子-物质相互作用在核心坍缩超新星 (CCSN) 爆炸中起着重要作用，因为它们有助于中微子和物质之间的轻子数和/或四动量交换，从而充当中微子驱动爆炸的代理。由于 CCSN 模拟中中微子输运的多尺度性质，需要对中微子-物质相互作用进行隐式处理，这需要在时间积分方案的每个步骤中求解耦合非线性系统。在本文中，我们设计并比较了隐式系统的非线性迭代求解器，该系统具有 CCSN 模拟中常用的能量耦合中微子-物质相互作用。具体来说，我们考虑电子中微子和反中微子，它们通过 Bruenn 85 不透明度集与静态物质配置相互作用。隐式系统源于中微子输运的非相对论两矩模型的离散化，该模型采用不连续伽辽金 (DG) 方法进行相空间离散化和隐式-显式 (IMEX) 时间积分方案。在这个 DG-IMEX 方案的背景下，我们提出了两种方法来制定非线性系统：耦合方法和嵌套方法。对于每种方法，生成的系统都使用安德森加速定点迭代和牛顿法求解。这四种迭代求解器的性能已经在具有不同程度碰撞的弛豫问题以及具有从球对称 CCSN 模拟中采用的几种物质分布的原中子星轻子化问题进行了比较。