Direct 3D Method of Characteristic Based on Efficient Characteristic Tracing and On-the-fly Generation
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摘要:
直接三维特征线方法（3D MOC）具有强大的几何处理能力，但是其对计算机的性能要求苛刻，尤其是极大的存储规模会限制机器适用性。为此，本文提出了一种基于层次建模树和改进R函数方法的特征线追踪方法，并在此基础上采用特征线信息实时生成（on-the-fly generation）技术，可有效降低计算时间和存储空间。对Takeda和C5G7算例的数值结果表明，在特征值等问题计算上与参考解相比具有良好的计算精度，提出的高效特征线追踪和实时生成方法能够显著降低存储空间，在分别付出增加约45%、23%的时间成本后，两个算例的存储空间分别最大可降低原来的99.51%、99.92%，证明了该方法可大大提高直接3D MOC的机器适用性。
Abstract:High-precision full reactor simulation is extremely important for reactor design and safety analysis. In recent years, three-dimensional (3D) full reactor transport calculation becomes one of the key development directions of deterministic calculation in reactor physics. 3D full reactor transport calculation requires the calculation program to have strong anisotropy, fine geometric processing and large-scale parallel computing capabilities. The method of characteristics (MOC) is one of the excellent implementations of the next generation of neutronic deterministic calculations due to its powerful geometric processing capabilities and natural parallelism. However, the huge requirements of the MOC for computing time and space storage are also important factors restricting development. The main technical routes of MOC include 2D/1D method and direct 3D method. Among them, the direct 3D MOC has powerful geometric processing capabilities, but its performance requirements for computers are harsh, especially the large storage scale will limit the applicability of the machine. To this end, a characteristic tracking method based on hierarchical modeling tree and improved R-function method was proposed, and on this basis, on-the-fly generation of characteristic information technology was adopted, which could effectively reduce computation time and spatial storage. The numerical results of the Takeda and C5G7 benchmarks show that the method have good computational accuracy compared to the reference solution in the calculation of eigenvalues and other benchmarks. The proposed efficient characteristic tracking and on-the-fly generation technology can significantly reduce spatial storage. After increasing the time cost by about 45% and 23% respectively, the storage of the two benchmarks can be reduced by up to 99.51% and 99.92%, respectively. It is proved that this method can greatly improve the machine applicability of the direct 3D MOC.
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图 4 C5G7算例的堆芯径向排布和边界条件
UO2—— UO2组件；MOX——MOX组件
Figure 4. Radial core arrangement and boundary condition of C5G7 benchmark
表 1 Takeda算例的keff计算结果
Table 1 keff result of Takeda benchmark
对比数据 case1 case2 keff 误差/pcm keff 误差/pcm 参考解 0.977 80(±60 pcm) 0.962 40(±60 pcm) 计算值 0.977 60 −20 0.962 57 17 
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表 2 Takeda case1算例各区域的平均通量
Table 2 Average flux of each region in Takeda case1 benchmark
对比数据 能群 空区 燃料区 反射层 平均通量 相对误差/% 平均通量 相对误差/% 平均通量 相对误差/% 参考解 1 1.450 0×10−3 4.750 9 ×10−35.9251 ×10−42 9.740 6×10−4 8.6998 ×10−49.1404 ×10−4计算值 1 1.464 3×10−3 0.98 4.7241 ×10−3−0.56 5.9489 ×10−40.40 2 9.537 2×10−4 −2.09 8.7009 ×10−40.01 8.8284 ×10−4−3.41
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表 3 Takeda case2算例各区域的平均通量
Table 3 Average flux of each region in Takeda case2 benchmark
对比数据 能群 控制棒 燃料区 反射层 平均通量 相对误差/% 平均通量 相对误差/% 平均通量 相对误差/% 参考解 1 1.224 7×10−3 4.9125 ×10−35.910 9 ×10−42 2.460 4×10−4 8.6921 ×10−48.7897 ×10−4计算值 1 1.224 9×10−3 0.01 4.8794 ×10−3−0.67 5.9305 ×10−40.33 2 2.514 9×10−4 2.21 8.6934 ×10−40.02 8.5151 ×10−4−3.12
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表 4 改变方位角的测试结果
Table 4 Test result of changed azimuth angle
极角
数量方位角
数量保存分段信息的
存储空间/MB实时生成的
存储空间/MB减少的空间
存储比/%保存分段信息的
计算时间/s实时生成的
计算时间/s时间增加
比例/%keff计算偏差/
pcm4 4 698.5 35.1 94.97 1 361.52 1 940.254 42.51 −166 4 8 1 218.2 35.1 97.12 3 145.536 4 590.991 45.95 −206 4 16 2 336.8 35.1 98.50 5 414.808 7 800.432 44.06 −199 4 32 4 589.6 35.1 99.24 11 571.95 16 628.77 43.70 −205
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表 5 改变密度测试结果
Table 5 Test result of changed density
（边长/特征线密度）/cm−1 保存分段信息的
存储空间/MB实时生成的
存储空间/MB减少的空间
存储比/%保存分段信息的
计算时间/s实时生成的
计算时间/s时间增加
比例/%keff计算偏差/
pcm5 339 35.1 89.65 745.362 1 066.985 7 43.15 −204 10 1 218.2 35.1 97.12 3 145.536 4 584.304 2 45.74 −206 15 2 661.1 35.1 98.68 5 816.61 8 399.184 8 44.40 −207 20 4 665.3 35.1 99.25 11 759.769 1 6 876.444 43.51 −207 25 7 223.9 35.1 99.51 18 146.043 25841.78 42.41 −207
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表 6 C5G7算例计算结果汇总
Table 6 Summary of calculation result for C5G7 benchmark
参数 参数值 算例参考解(MCNP) MOC keff 1.186 55 1.185 19 keff误差，pcm −136 AVG，% 0.32 0.435 RMS，% 0.34 0.596 MRE，% 0.27 0.376 最大栅元归一化功率 2.498 2.505 最大栅元功率相对误差，% ±0.16 0.28 最小栅元归一化功率 0.232 0.236 最小栅元功率相对误差，% ±0.58 1.72 栅元最大相对误差，% 3.90
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表 7 2个极角和4个方位角下的计算时间和存储空间
Table 7 Calculation time and storage requirement of 2 polar and 4 azimuth angles
求积组 保存分段信息的
存储空间/MB实时生成的
存储空间/MB减少的空间
存储比/%保存分段信息的
计算时间/s实时生成的
计算时间/s时间增加
比例/%keff计算偏差/
pcm(2,4)
(8,16)6 940
111 04084
8498.79
99.9282 576
1 215 955101 386
1 492 95022.78
22.78−434
−136
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