基于C5G7-MOX的中子输运计算方法比较及MOC参数敏感性初步分析

Comparison of neutron transport calculation methods based on C5G7-MOX and preliminary analysis of sensitivity of MOC parameters

特征线方法(Method of Characteristics,MOC)因其具备强大的几何处理能力,且在计算过程中亦能兼顾计算成本和计算精度,被广泛应用于高保真数值模拟计算中。常见的中子输运计算方法除MOC外,还包括碰撞概率法(Collision Probability method,CP)和界面流法(Interface Current method,IC)等。本文从方法理论以及数值计算两方面将MOC、CP和IC进行比较分析,评估其在pin-by-pin计算中的能力。同时在MOC计算中,不同的参数选择会对计算成本和计算精度产生影响,因此有必要进行敏感性分析以寻求最佳参数。本文首先将三种计算方法从原理上进行比较分析,再基于2D C5G7-MOX基准题完成了数值计算及MOC参数敏感性初步分析。计算结果表明:MOC在计算精度、计算效率和内存开销上均优于CP和IC。MOC的计算耗时和内存开销分别为23.9 min和37.5 MB,与参考解的相对误差仅为6.04×10^(-4)。而CP和IC的计算耗时分别为MOC的56.7倍和15.6倍,内存开销分别为MOC的407.7倍和32.8倍。进一步通过参数敏感性分析发现:网格划分对计算内存开销以及计算时间的影响最大,而极角的选择对计算精度的影响最大,并且给出一组综合优化建议参数:网格划分6×6,极角为GAUS且数目为2,方位角个数为30。该组参数的计算耗时为45.4 min,内存开销为264.7 MB,相对误差为5.9×10^(-5),归一化后的栅元均方根误差为0.002 55。

[Background]The Method of Characteristics(MOC)is widely applied to high-fidelity numerical simulations due to its robust geometric processing capabilities,as well as its ability to balance computational costs and accuracy during calculations.In addition to MOC,common neutron transport calculation methods also include the Collision Probability method(CP)and the Interface Current method(IC).In MOC calculation,different parameter selections will lead to different values of calculation cost and accuracy.[Purpose]This paper aims to evaluate the ability of MOC,CP and IC methods for pin-by-pin calculation,and conduct sensitivity analysis to find the best parameter setting for MOC method.[Methods]The three aforementioned calculation methods were compared from the perspective of theory and numerical calculation.Subsequently,numerical calculation and preliminary analysis of the sensitivity of MOC parameters were conducted based on the 2D C5G7-MOX reference problem.[Results]Numerical calculation results show that the computation time and memory cost incur by the MOC are 23.9 min and 37.5 MB,respectively,and the relative error between the MOC results and reference solutions is only 6.04×10^(-4).The computing times of the CP and IC methods are 56.7 times and 15.6 times that of the MOC,and the memory costs are 407.7 times and 32.8 times that of the MOC,respectively.As a result of the sensitivity analysis of MOC parameters,the following set of parameters is suggested:a grid division of 6×6,a pole angle of GAUS,a pole number of 2,and an azimuth angle of 30°.The calculation time and the memory cost of this set of parameters are 45.4 min and 264.7 MB,respectively,with the relative error of 5.9×10^(-5) and the normalized RMS error of 0.00255.[Conclusions]The results of this study indicate that the MOC is superior to the CP and IC methods in accuracy,efficiency,and memory cost,and the grid division of MOC has the greatest influence on the calculation memory cost and calculation time whereas the choice of polar angle has the greatest influence on the calculation accuracy.With its powerful geometric processing ability and consideration of the calculation cost and accuracy,the MOC is more widely used in high-fidelity numerical simulation for neutron transport calculation.