Second Moment Methods (SMMs) are developed that are consistent with the Discontinuous Galerkin (DG) spatial discretization of the discrete ordinates (or \Sn) transport equations. The low-order (LO) diffusion system of equations is discretized with fully consistent \Pone, Local Discontinuous Galerkin (LDG), and Interior Penalty (IP) methods. A discrete residual approach is used to derive SMM correction terms that make each of the LO systems consistent with the high-order (HO) discretization. We show that the consistent methods are more accurate and have better solution quality than independently discretized LO systems, that they preserve the diffusion limit, and that the LDG and IP consistent SMMs can be scalably solved in parallel on a challenging, multi-material benchmark problem.

翻译：发展了与离散纵标（\Sn）输运方程的不连续伽辽金（DG）空间离散格式一致的二阶矩方法（SMM）。低阶（LO）扩散方程组采用完全一致的\Pone、局部不连续伽辽金（LDG）和内罚（IP）方法进行离散化。利用离散残差方法推导SMM修正项，使每个低阶系统与高阶（HO）离散格式保持一致。研究表明：与独立离散化的低阶系统相比，一致方法具有更高的精度和更优的解质量，能保持扩散极限，并且LDG和IP一致SMM方法可在具有挑战性的多材料基准问题上实现可扩展并行求解。