AI 中文总结
提出一种基于宏微观分量解耦的混合蒙特卡罗/确定论方法，通过固定点迭代求解双层方程，实现随机数值解的方差缩减和计算效率提升。
AI 中文摘要
本文提出一种新的混合蒙特卡罗/确定论方法，用于求解单群稳态玻尔兹曼输运方程，该方法基于解在宏观和微观分量上的分解。宏观分量捕捉解的大尺度结构，由高阶输运解的角矩表示。采用$P_1$近似定义宏观分量，前两个角矩作为具有精确闭合的混合低阶矩方程的解获得。微观分量的方程使用蒙特卡罗模拟求解。宏微观分量的混合双层方程组通过固定点迭代格式求解。数值结果展示了随机数值解的方差缩减和计算效率的提升。
英文摘要
This paper presents a new hybrid MC/deterministic method for solving the one-group steady-state Boltzmann transport equation based on decomposition of solution in macro and micro components. The macro component captures the large-scale structure of the solution. It is represented by angular moments of the high-order transport solution. The $P_1$ approximation is applied to define the macro component. The first two angular moments are obtained as a solution of hybrid low-order moment equations with exact closures. The equation for the micro component is solved using a MC simulation. The hybrid two-level system of equations for macro and micro components is solved by fixed-point iteration scheme. Numerical results are presented to demonstrate variance reduction of stochastic numerical solution and improvement in computational efficiency.
Comments9 pages, 6 figures, 2 tables
