We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to convert existing discretizations of the VEF moment system to discretizations of the SMM moment system. The moment discretizations are coupled to a high-order Discontinuous Galerkin discretization of the Discrete Ordinates transport equations. We show that the resulting methods achieve high-order accuracy on high-order (curved) meshes, preserve the thick diffusion limit, and are effective on a challenging multi-material problem both in outer fixed-point iterations and in inner preconditioned iterative solver iterations for the discrete moment systems. We also present parallel scaling results and provide direct comparisons to the VEF algorithms the SMM algorithms were derived from.

翻译：用于线性输运问题的高阶有限元二阶矩方法 翻译后的摘要： 我们提出了基于高阶有限元的二阶矩方法（SMM）来解决二维辐射输运问题。我们利用可变 Eddington 因子（VEF）方法和 SMM 之间的紧密联系，将现有的 VEF 矩系统的离散化转化为 SMM 矩系统的离散化。矩离散化与不连续 Galerkin 离散化的离散有序传输方程相耦合。我们表明，所得到的方法在高阶（曲面）网格上实现高阶精度、保持厚对比度极限，并且在具有挑战性的多材料问题中是有效的，无论是在外固定点迭代中还是在内部预处理迭代求解器迭代中进行离散时刻系统。我们还提供了并行缩放结果，并直接将 SMM 算法与其衍生自的 VEF 算法进行比较。