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

Journals >NUCLEAR TECHNIQUES >Volume 47 >Issue 2 >Page 020604 > Article

NUCLEAR TECHNIQUES
Vol. 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

show less

DOI: 10.11889/j.0253-3219.2024.hjs.47.020604 Cite this Article

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 Copy Citation Text

show less

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

Download full size | View in the Article

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)

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)

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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
1	2	0.4	0.15	0.2	0.01
2	1	1.4	0.01	0.007	0.01
2	2	0.4	0.15	0.2	0.01
3	1	1.3	0.008	0.003	0.01
3	2	0.5	0.05	0.06	0.01

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

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

$λ$ 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 3. Eigenvalues and energy ratios corresponding to POD basis

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

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

Download Citation

Save the article for my favorites

Paper Information