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：我们提出了基于高阶有限元的方法（二阶矩方法，SMMs），用于求解二维空间中的辐射传输问题。通过利用变爱丁顿因子（VEF）方法与SMM之间的紧密联系，我们将现有的VEF矩系统离散化方法转换为SMM矩系统的离散化方法。这些矩离散化与离散纵标传输方程的高阶间断伽辽金（Discontinuous Galerkin）离散化相结合。研究表明，所提出的方法能够在高阶（曲线）网格上实现高阶精度，保持厚扩散极限，并且在外部固定点迭代和内部预处理迭代求解器迭代中，对具有挑战性的多材料问题均表现出有效性。我们还给出了并行扩展结果，并与所导出的SMM算法的基础VEF算法进行了直接比较。