Abstract

The convergence performance of nonlinear acceleration methods for the method of characteristics (MOC) with flat source (FS) approximation (FS MOC) or linear source (LS) approximation (LS MOC) is numerically investigated by focusing on the spatial and angular approximations in the acceleration calculations. The convergence of nonlinear acceleration depends on the consistency of the calculation models between the higher-order and lower-order (acceleration) methods. The convergence of four acceleration methods is evaluated to clarify the relationship between model consistency and convergence performance. These methods consist of FS or LS for the spatial source distribution and P1 or discrete angle for the angular distribution, i.e., (1) FS analytic coarse mesh finite difference (ACMFD) acceleration (FS ACMFD), (2) LS ACMFD, (3) FS angular-dependent discontinuity factor MOC (ADMOC) acceleration (FS ADMOC), and (4) LS ADMOC. The ACMFD and ADMOC accelerations are based on P1 and discrete angle approximations, respectively. The FS MOC and LS MOC are considered higher-order methods. The FS MOC and LS MOC with five acceleration methods, i.e., the aforementioned four acceleration methods and the conventional coarse mesh finite difference acceleration method, are used to perform fixed-source calculations in one-group one-dimensional homogeneous slab geometry, and the spectral radii are numerically evaluated. The numerical results indicate that (1) the nonlinear acceleration methods that are unconditionally stable for FS MOC also show similar convergence properties for LS MOC in one-dimensional slab geometry; (2) better convergence is observed when the consistency of higher- and lower-order models is high; and (3) when a coarse mesh is optically thick, the spatial homogenization degrades the convergence performance, even if spatial and angular approximations are consistent between the higher- and lower-order models.

摘要

以平面源（FS）逼近（FS MOC）或线性源（LS）逼近（LS MOC）的特征法（MOC）的非线性加速方法的收敛性能为重点，通过关注空间和角度逼近加速度计算。非线性加速度的收敛取决于高阶和低阶（加速度）方法之间计算模型的一致性。评估四种加速方法的收敛性，以阐明模型一致性和收敛性能之间的关系。这些方法包括空间源分布的 FS 或 LS 和角度分布的 P1 或离散角度，即（1）FS 解析粗网格有限差分（ACMFD）加速度（FS ACMFD），（2）LS ACMFD，(3) FS 角度相关不连续因子 MOC (ADMOC) 加速度 (FS ADMOC)，和 (4) LS ADMOC。ACMFD 和 ADMOC 加速度分别基于 P1 和离散角度近似值。FS MOC 和 LS MOC 被认为是高阶方法。FS MOC和LS MOC具有五种加速方法，即上述四种加速方法和常规粗网格有限差分加速方法，用于在一组一维齐次板几何中进行固定源计算，谱半径是用数值计算的。数值结果表明：（1）对于 FS MOC 无条件稳定的非线性加速方法也表现出与 LS MOC 在一维板坯几何中相似的收敛特性；(2) 当高阶和低阶模型的一致性高时，观察到更好的收敛性；(3) 当粗网格在光学上很厚时，空间均匀化会降低收敛性能，即使空间和角度近似在高阶和低阶模型之间是一致的。