A two-dimensional finite element shielding calculation code with mass-matrix lumping technique and unstructured meshes

Zhiwei ZONG; Maosong CHENG

doi:10.11889/j.0253-3219.2023.hjs.46.020602

Journals >NUCLEAR TECHNIQUES >Volume 46 >Issue 2 >Page 020602 > Article

NUCLEAR TECHNIQUES
Vol. 46, Issue 2, 020602 (2023)

A two-dimensional finite element shielding calculation code with mass-matrix lumping technique and unstructured meshes

Zhiwei ZONG and Maosong CHENG^*

Author Affiliations

Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China

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DOI: 10.11889/j.0253-3219.2023.hjs.46.020602 Cite this Article

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 Copy Citation Text

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Fig. 1. Calculation flowchart of ThorSNIPE

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Fig. 2. Geometry of BWR cell benchmark

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Fig. 3. Geometry of Argonne-5-A1 benchmark

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Fig. 4. Scalar flux distribution of group 1 (a) CGFEM-no, (b) CGFEM-mass, (c) DGFEM-no

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Fig. 5. Scalar flux distribution of group 2 (a) CGFEM-no, (b) CGFEM-mass, (c) DGFEM-no

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Fig. 6. Percent deviation of calculated value and reference value of group 1 (a) and group 2 (b)

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Fig. 7. Geometric structure diagram of Dog leg duct benchmark

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Fig. 8. Correlation comparison between L₂-error norm and mesh computing under different calculation models

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Fig. 9. Scalar fluxes distribution (a) and percent deviation of scalar fluxes (b) along Y at X=6.0 cm

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区域 Region	能群 Group	总截面 Σ_t / cm^-1	散射截面 Σ_s,g_→1 / cm^-1	散射截面 Σ_s,g_→2 / cm^-1	裂变截面 υΣ_s_,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 1. Isotropic cross sections

计算模型 Calculation models	能群1 Group 1			能群2 Group 2				k_eff	相对偏差 Relative error	时间 Time / s
计算模型 Calculation models	R1	R2	相对偏差 Relative error	R1	相对偏差 Relative error	R2	相对偏差 Relative error	k_eff	相对偏差 Relative error	时间 Time / s
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 2. Average scalar fluxes and eigenvalues in regions 1 and 2

能群

Group

总截面

Σ_t / cm^-1

散射截面

Σ_s,g_→1 / cm^-1

散射截面

Σ_s,g_→2 / cm^-1

源强密度

Source density / n·cm^-2·s^-1

9.210 40×10^-2

6.947 0×10^-3

6.546 0×10^-3

1.008 77×10^-1

2.343 4×10^-2

4.850 0×10^-3

1.770 1×10^-2

Table 3. Isotropic cross sections and source density

材料Material

总截面Σ_t / cm^-1

散射截面Σ_s / cm^-1

源强密度Source density / n·cm^-2·s^-1

0.5

0.0

1.0

0.5

0.0

0.5

0.0

Table 4. Isotropic cross sections and source density

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

Table 5. Strict non-negativity under different calculation models

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

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