NUCLEAR TECHNIQUES, Volume. 46, Issue 2, 020602(2023)
A two-dimensional finite element shielding calculation code with mass-matrix lumping technique and unstructured meshes
Figures & Tables(14)
Fig. 4. Scalar flux distribution of group 1 (a) CGFEM-no, (b) CGFEM-mass, (c) DGFEM-no
Fig. 5. Scalar flux distribution of group 2 (a) CGFEM-no, (b) CGFEM-mass, (c) DGFEM-no
Fig. 6. Percent deviation of calculated value and reference value of group 1 (a) and group 2 (b)
Fig. 8. Correlation comparison between L2-error norm and mesh computing under different calculation models
Fig. 9. Scalar fluxes distribution (a) and percent deviation of scalar fluxes (b) along Y at X=6.0 cm
Table 1. Isotropic cross sections
View tableView in ArticleTable 1. Isotropic cross sections
区域
Region
能群
Group
总截面
Σt / cm-1
散射截面
Σs,g→1 / cm-1
散射截面
Σs,g→2 / cm-1
裂变截面
υΣs,1→g / cm-1
R1 1 1.966 47×10-1 1.780×10-1 1.002×10-2 6.203×10-3 2 5.961 59×10-1 1.089×10-3 5.255×10-1 1.101×10-1 R2 1 2.220 64×10-1 1.995×10-1 2.188×10-2 0 2 8.878 74×10-1 1.558×10-3 8.783×10-1 0
Table 2. Average scalar fluxes and eigenvalues in regions 1 and 2
View tableView in ArticleTable 2. Average scalar fluxes and eigenvalues in regions 1 and 2
计算模型
Calculation models
能群1 Group 1 能群2 Group 2 keff 相对偏差
Relative
error
时间
Time / s
R1 R2 相对偏差
Relative
error
R1 相对偏差
Relative
error
R2 相对偏差
Relative
error
Reference 1.0 0.926 9 ― 0.352 7 ― 0.451 4 ― 1.212 7 ― ― CGFEM(S4) 1.0 0.938 6 0.012 6 0.918 4 -0.009 2 0.463 6 0.027 0 1.215 1 0.002 0 7.1 CGFEM(S8) 1.0 0.923 5 -0.003 7 0.359 5 0.019 4 0.459 3 0.017 5 1.214 0 0.001 0 25.7 CGFEM(S16) 1.0 0.918 4 -0.009 2 0.355 1 0.006 8 0.457 4 0.013 2 1.213 3 0.000 5 95.4 DGFEM(S4) 1.0 0.944 1 0.018 6 0.364 0 0.032 0 0.464 3 0.028 6 1.215 1 0.001 9 46.2 DGFEM(S8) 1.0 0.930 1 0.003 5 0.358 9 0.017 5 0.461 1 0.021 5 1.213 7 0.000 8 139.3 DGFEM(S16) 1.0 0.925 0 -0.002 1 0.357 6 0.013 8 0.459 5 0.017 9 1.213 2 0.000 4 463.4
Table 3. Isotropic cross sections and source density
View tableView in ArticleTable 3. Isotropic cross sections and source density
能群
Group
总截面
Σt / cm-1
散射截面
Σs,g→1 / cm-1
散射截面
Σs,g→2 / cm-1
源强密度
Source density / n·cm-2·s-1
1 9.210 40×10-2 6.947 0×10-3 0 6.546 0×10-3 2 1.008 77×10-1 2.343 4×10-2 4.850 0×10-3 1.770 1×10-2
Table 4. Isotropic cross sections and source density
View tableView in ArticleTable 4. Isotropic cross sections and source density
材料Material 总截面Σt / cm-1 散射截面Σs / cm-1 源强密度Source density / n·cm-2·s-1 R1 0.5 0.0 1.0 R2 0.5 0.0 0.0 R3
R4
0.0
0.5
0.0
0.0
0.0
0.0
Table 5. Strict non-negativity under different calculation models
View tableView in ArticleTable 5. Strict non-negativity under different calculation models
网格尺度
Mesh diameter
网格数
Mesh number
计算模型Calculation models CGFEM-no CGFEM-mass DGFEM-no DGFEM-mass 0.2
0.25
0.5
1.0
1.5
2.0
2.5
3.0
5.0
14 904
9 516
2 432
632
290
197
171
94
71
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Zhiwei ZONG, Maosong CHENG. A two-dimensional finite element shielding calculation code with mass-matrix lumping technique and unstructured meshes[J]. NUCLEAR TECHNIQUES, 2023, 46(2): 020602
Paper Information
Category: Research Articles
Received: Aug. 5, 2022
Accepted: --
Published Online: Mar. 2, 2023
The Author Email: CHENG Maosong (mscheng@sinap.ac.cn)
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