角度相关共轭函数的蒙卡自动减方差算法研究

Research on Monte Carlo Variance Reduction Algorithm for the Angle-Dependent Adjoint Function

摘要: 一致性共轭驱动重要抽样(CADIS)方法是目前广泛采用的自动减方差方法，该方法采用共轭标通量密度来一致性生成减方差参数，但缺乏角度偏倚信息，在处理角通量密度各向异性强的屏蔽问题时加速效果受到限制。本文基于CADIS-Ω方法，以多维离散纵标输运计算程序ARES为载体，开发角度相关减方差参数计算模块，构造正向加权重要性函数，自动生成角度相关源偏倚参数与权窗参数，弥补现有减方差参数在角度信息上的缺失，为蒙卡求解强各向异性深穿透屏蔽问题提供匹配度更高的自动减方差参数。采用IRI-TUB国际基准题进行验证。数值结果表明，CADIS-Ω方法能够在保证结果无偏的情况下获得较CADIS方法更优的加速效果。初步验证可说明CADIS-Ω方法对于复杂的强各向异性深穿透问题具有较好的应用前景。

Abstract: Consistent Adjoint Driven Importance Sampling (CADIS) is a widely utilized automatic variance reduction method. This method employs adjoint scalar flux to consistently generate variance reduction parameters. However, it lacks angle biasing information and its acceleration effect is limited when dealing with deep-penetration shielding problems characterized by strong anisotropy. Building upon the CADIS-Ω method and utilizing the multi-dimensional discrete ordinates transport calculation code ARES, this paper develops a calculation module for angle-dependent variance reduction parameters. It constructs a forward-weighted importance function and automatically generates angle-dependent source biasing parameters and weight window parameters to compensate for the absence of angle information in existing variance reduction parameters. This paper introduces a variance reduction parameter with a higher matching degree for solving the strong anisotropic deep penetration shielding problem by MCNP. The international benchmark problem IRI-TUB was used for verification purposes. Numerical results demonstrate that the CADIS-Ω method can achieve better acceleration effects compared to the CADIS method without biasing. Preliminary verification indicates that the CADIS-Ω method holds promising potential for addressing complex strong anisotropic deep penetration problems.