Apply implicitly restarted Arnoldi method to solving eigenvalue problem and reducing dimensionality in neutron diffusion

Zhaocai XIANG; Qiafeng CHEN; Pengcheng ZHAO; Qinghang ZHANG

doi:10.11889/j.0253-3219.2024.hjs.47.020604

NUCLEAR TECHNIQUES, Volume. 47, Issue 2, 020604(2024)

Apply implicitly restarted Arnoldi method to solving eigenvalue problem and reducing dimensionality in neutron diffusion

Zhaocai XIANG, Qiafeng CHEN, Pengcheng ZHAO^*, and Qinghang ZHANG

Author Affiliations

School of Nuclear Science and Technology, University of South China, Hengyang 421001, China

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Figures & Tables(8)

Fig. 1. TWIGL benchmark problem area division, geometric dimensions, and boundary conditions

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Fig. 2. Distribution of the first three harmonics for fast and thermal groups when the absorption cross-section of Zone 1 is 0.148, solved by IRAM (color online)

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Fig. 3. TWIGL benchmark problem core neutron flux distribution for fast group (a) and thermal group (b) (color online)

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Fig. 4. Diagonal neutron dose rate distribution and comparison with reference solution for fast group (a) and thermal group (b)

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Table 1. Physical parameters of two-dimensional steady-state TWIGL benchmark problem
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Table 1. Physical parameters of two-dimensional steady-state TWIGL benchmark problem
材料
Materials
能群
Energy group
D_g
/ cm
Σ_a_,_g
/ cm^-1
Σ_f_,_g
/ n·cm^-1
νΣ_z_,1→2
/ cm^-1
1 1 1.4 0.01 0.007 0.01
2 0.4 0.15 0.2
2 1 1.4 0.01 0.007 0.01
2 0.4 0.15 0.2
3 1 1.3 0.008 0.003 0.01
2 0.5 0.05 0.06

Table 2. Calculation results and relative deviations of the first six eigenvalues for different cross-sections

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Table 2. Calculation results and relative deviations of the first six eigenvalues for different cross-sections

$k$ 本征值阶数 Order of $k$	$k$ 本征值Eigenvalues （ $\sum_{a, 2}$ =0.148 cm^-1）	误差Error $ε_{i}$ / 10^-14	$k$ 本征值Eigenvalues （ $\sum_{a, 2}$ =0.149 cm^-1）	误差Error $ε_{i}$ / 10^-14
1	0.915 294	4.177 633	0.914 300	7.026 130
2	0.757 646	3.740 520	0.757 392	5.080 474
3	0.704 921	5.079 273	0.703 748	5.396 081
4	0.600 850	3.310 676	0.600 447	3.593 584
5	0.523 297	6.168 209	0.522 959	6.521 626
6	0.514 429	4.177 633	0.513 680	4.403 287

Table 3. Eigenvalues and energy ratios corresponding to POD basis

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Table 3. Eigenvalues and energy ratios corresponding to POD basis

$λ$ 本征值阶数 Order of $λ$	$λ$ 本征值 $λ$ eigenvalues	能量占比 Energy proportion / %
1	2.324 431	19.370 260
2	2.042 215	17.018 458
3	2.010 894	16.757 455
4	1.957 768	16.314 740
5	1.888 873	15.740 611
6	1.775 744	14.797 871
7⁓12	0.000 072	0.000 347 7

Table 4. Calculation results of the first six eigenvalues for the TWIGL benchmark problem core
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Table 4. Calculation results of the first six eigenvalues for the TWIGL benchmark problem core
k本征值阶数Order of k k本征值k eigenvalues $ε_{i}$ 误差 $ε_{i}$ error
1 0.913 127 0.000 189
2 0.758 656 0.001 528
3 0.703 665 0.002 000
4 0.602 489 0.004 081
5 0.569 520 0.077 694
6 0.552 796 0.089 719

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Zhaocai XIANG, Qiafeng CHEN, Pengcheng ZHAO, Qinghang ZHANG. Apply implicitly restarted Arnoldi method to solving eigenvalue problem and reducing dimensionality in neutron diffusion[J]. NUCLEAR TECHNIQUES, 2024, 47(2): 020604

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Paper Information

Category: Research Articles

Received: May. 10, 2023

Accepted: --

Published Online: Apr. 24, 2024

The Author Email: ZHAO Pengcheng (赵鹏程)

DOI:10.11889/j.0253-3219.2024.hjs.47.020604

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Table 1. Physical parameters of two-dimensional steady-state TWIGL benchmark problem

Table 1. Physical parameters of two-dimensional steady-state TWIGL benchmark problem

Table 2. Calculation results and relative deviations of the first six eigenvalues for different cross-sections

Table 2. Calculation results and relative deviations of the first six eigenvalues for different cross-sections

Table 3. Eigenvalues and energy ratios corresponding to POD basis

Table 3. Eigenvalues and energy ratios corresponding to POD basis

Table 4. Calculation results of the first six eigenvalues for the TWIGL benchmark problem core

Table 4. Calculation results of the first six eigenvalues for the TWIGL benchmark problem core