Abstract Strong flux attenuation and intense material heterogeneity are extremely challenging conundrums of discrete ordinates transport calculations for neutron or gamma deep-penetration shielding problems. The spatial discretization methods of high accuracy and strong robustness are indispensable for varying materials, including absorbers and cavities, and for meshes of large or small size. A family of the characteristic-based spatial schemes is chosen to construct a suit of the stable and efficient transport architecture for the nuclear installation shielding problems. The reformulations of a series of the characteristic-based schemes are presented based on Cartesian hexahedron grids. The related optimizations are proposed about parameter calculation, solving procedure and stability improvement for higher accuracy and efficiency. Numerical results and evaluations are given for several monoenergetic benchmarks and self-designed problems. The behaviors of the short characteristic and the zero-order finite difference schemes are compared for meshes of different optical thicknesses. The linear and exponential short characteristic schemes exhibit excellent accuracy advantages over the tested cell-average-based discretization methods. The slice-balance-approach-based DD-like scheme is more accurate and stable than the constant short characteristic method. Exponential short characteristic method possesses the best coarse mesh accuracy with RMS error norms slightly higher than 10% using 10-times-optical-thickness grids for the self-designed streaming-dominated deep-penetration problem.

中文翻译：

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结构六面体网格离散纵坐标方程鲁棒特征离散化的重构与评价

摘要 强通量衰减和强烈的材料异质性是中子或伽马深穿透屏蔽问题离散纵坐标输运计算中极具挑战性的难题。高精度和强鲁棒性的空间离散化方法对于各种材料（包括吸收体和腔体）以及大小网格都是必不可少的。选择了一系列基于特征的空间方案，为核设施屏蔽问题构建一套稳定高效的运输架构。基于笛卡尔六面体网格提出了一系列基于特征的方案的重新表述。对参数计算、求解过程和稳定性提高等方面提出了相关优化，以提高精度和效率。给出了几个单能基准和自行设计的问题的数值结果和评估。比较了不同光学厚度网格的短路特性和零阶有限差分格式的行为。线性和指数短路特征方案比基于单元平均的离散化方法表现出优异的精度优势。基于slice-balance-approach的DD-like方案比恒定短路特性方法更准确和稳定。指数短特征方法具有最好的粗网格精度，RMS 误差范数略高于 10%，使用 10 倍光厚网格解决自行设计的流主导的深穿透问题。比较了不同光学厚度网格的短路特性和零阶有限差分格式的行为。线性和指数短路特征方案比基于单元平均的离散化方法表现出优异的精度优势。基于slice-balance-approach的DD-like方案比恒定短路特性方法更准确和稳定。指数短特征方法具有最好的粗网格精度，RMS 误差范数略高于 10%，使用 10 倍光厚网格解决自行设计的流主导的深穿透问题。比较了不同光学厚度网格的短路特性和零阶有限差分格式的行为。线性和指数短路特征方案比基于单元平均的离散化方法表现出优异的精度优势。基于slice-balance-approach的DD-like方案比恒定短路特性方法更准确和稳定。指数短特征方法具有最好的粗网格精度，RMS 误差范数略高于 10%，使用 10 倍光厚网格解决自行设计的流主导的深穿透问题。线性和指数短路特征方案比基于单元平均的离散化方法表现出优异的精度优势。基于slice-balance-approach的DD-like方案比恒定短路特性方法更准确和稳定。指数短特征方法具有最好的粗网格精度，RMS 误差范数略高于 10%，使用 10 倍光厚网格解决自行设计的流主导的深穿透问题。线性和指数短路特征方案比基于单元平均的离散化方法表现出优异的精度优势。基于slice-balance-approach的DD-like方案比恒定短路特性方法更准确和稳定。指数短特征方法具有最好的粗网格精度，RMS 误差范数略高于 10%，使用 10 倍光厚网格解决自行设计的流主导的深穿透问题。