Abstract Obtaining sufficiently accurate geometric descriptions is a crucial prerequisite for reliable particle transport calculations. Conventional transport algorithms on Cartesian grids use a highly efficient sweep technique and numerous mature discretization methods despite their modeling deficiency for complex geometries. To achieve a more accurate geometric description, a cell-based nonmatching Cartesian grid algorithm is proposed on the basis of the multilevel octree architecture. Transport sweep is performed according to the tree branch relationship of nested mesh distributions. The angular flux transmission between discontinuous grids is handled by the flux spatial moment mapping technique, and multiple zero-order mapping schemes are developed, including finite element interpolation, distance interpolation, and exponential fitting methods for treating upwind flux distributions of different relative shapes. The first-order mapping schemes are modified and improved for linear and exponential short characteristic discretization methods. The mapping accuracy is evaluated for polynomial and exponential functions, and a new spatial shape factor is presented for measuring the degree of nonlinearity. The multilevel octree grid (MLTG) algorithm is tested for neutron transport benchmarks, and good agreement with Monte Carlo and standard SN results is achieved. The number of meshes in the VVER shielding model is reduced from 18 million to 2 million using 3-level octree grids with the same geometric description accuracy. Numerical verification of a one-group fixed-source problem shows that 4-level and 5-level MLTG results with proper spatial discretization schemes can achieve relative deviations of less than 3% and 5% for detector region flux, respectively.

中文翻译：

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基于多级八叉树结构的离散坐标输运计算的非匹配不连续笛卡尔网格算法

摘要 获得足够精确的几何描述是可靠的粒子输运计算的关键先决条件。笛卡尔网格上的传统传输算法使用高效的扫描技术和众多成熟的离散化方法，尽管它们对复杂几何的建模存在缺陷。为了实现更精确的几何描述，在多级八叉树结构的基础上，提出了一种基于单元的非匹配笛卡尔网格算法。传输扫描是根据嵌套网格分布的树分支关系进行的。利用磁通空间矩映射技术处理不连续网格之间的角磁通传递，开发了多种零阶映射方案，包括有限元插值、距离插值、和指数拟合方法处理不同相对形状的逆风通量分布。对线性和指数短特征离散化方法的一阶映射方案进行了修改和改进。对多项式和指数函数的映射精度进行了评估，并提出了一种新的空间形状因子来衡量非线性程度。多级八叉树网格 (MLTG) 算法针对中子输运基准进行了测试，并且与蒙特卡罗和标准 SN 结果取得了良好的一致性。使用具有相同几何描述精度的 3 级八叉树网格，VVER 屏蔽模型中的网格数从 1800 万减少到 200 万。