利用线性不连续源倾斜和有效散射与裂变率计数来缓解中子输运模拟中迭代准蒙特卡洛（iQMC）方法的空间误差
Mitigating Spatial Error in the iterative-Quasi-Monte Carlo (iQMC) Method for Neutron Transport Simulations with Linear Discontinuous Source Tilting and Effective Scattering and Fission Rate Tallies
AI总结：
本文针对迭代准蒙特卡洛（iQMC）方法在中子输运模拟中的网格空间离散误差问题，提出有效源输运扫描和基于历史的线性不连续源倾斜两项改进，显著降低了全局计数和本征值误差。
摘要：
迭代准蒙特卡洛（iQMC）方法是近期提出的一种用于多群中子输运模拟的方法。iQMC可被视为确定性迭代技术、蒙特卡洛模拟与准蒙特卡洛技术的混合体。iQMC具备多项适合高性能计算环境的算法特性，包括$O(N^{-1})$收敛方案、射线追踪输运扫描，以及类似于模拟蒙特卡洛的高度可并行化特性。尽管使用iQMC具有诸多潜在优势，但也存在固有缺点，即由于在整个区域使用网格而引入的空间离散误差。本文对iQMC引入了两项重要修改以帮助减少空间离散误差。第一项是有效源输运扫描，即通过额外计数实时更新源强度。该版本的输运扫描本质上与网格、材料和几何形状无关。第二项是引入基于历史的线性不连续源倾斜方法。传统上，iQMC在网格的每个单元中使用分段常数源。然而，通过所提出的源倾斜技术，iQMC能在每个单元中使用分段线性源，从而在不细化网格的情况下减少空间误差。文中展示了来自2D C5G7和Takeda-1 k-本征值基准问题的数值结果。结果表明，基于历史的源倾斜显著减少了两个基准中全局计数和本征值解的误差。通过有效源输运扫描和线性源倾斜，iQMC能够在仅有$204\times204$个单元的均匀笛卡尔网格上，将2D C5G7问题的本征值收敛至误差小于$0.04\%$。
英文摘要：
The iterative Quasi-Monte Carlo (iQMC) method is a recently proposed method for multigroup neutron transport simulations. iQMC can be viewed as a hybrid between deterministic iterative techniques, Monte Carlo simulation, and Quasi-Monte Carlo techniques. iQMC holds several algorithmic characteristics that make it desirable for high performance computing environments including a $O(N^{-1})$ convergence scheme, ray tracing transport sweep, and highly parallelizable nature similar to analog Monte Carlo. While there are many potential advantages of using iQMC there are also inherent disadvantages, namely the spatial discretization error introduced from the use of a mesh across the domain. This work introduces two significant modifications to iQMC to help reduce the spatial discretization error. The first is an effective source transport sweep, whereby the source strength is updated on-the-fly via an additional tally. This version of the transport sweep is essentially agnostic to the mesh, material, and geometry. The second is the addition of a history-based linear discontinuous source tilting method. Traditionally, iQMC utilizes a piecewise-constant source in each cell of the mesh. However, through the proposed source tilting technique iQMC can utilize a piecewise-linear source in each cell and reduce spatial error without refining the mesh. Numerical results are presented from the 2D C5G7 and Takeda-1 k-eigenvalue benchmark problems. Results show that the history-based source tilting significantly reduces error in global tallies and the eigenvalue solution in both benchmarks. Through the effective source transport sweep and linear source tilting iQMC was able to converge the eigenvalue from the 2D C5G7 problem to less than $0.04\%$ error on a uniform Cartesian mesh with only $204\times204$ cells.
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