Application of JFNK Method in SN Transport Calculations

doi:10.19596/j.cnki.1001-246x.8282

Abstract

Abstract:

JFNK method is an efficient method for nonlinear problems. We consider two nonlinearities of neutron transport equation, the negative flux correction and the k-eigenvalue problem. The nonlinear problems are transformed into nonlinear residual equation form. And then we use JFNK method to solve them. We analyze impact of different constraints on the performance of JFNK, and compare JFNK method with NK method. LGMRES is used instead of restarting GMRES(m) method. Numerical results show that: ① Compared with SI method, JFNK has higher computational efficiency, even in the case of high scattering ratio; ② Difference approximation of Jacobian matrix-vector multiplication has no effect on the result, and the physics-based constraints are more efficient than standard mathematical constraints; ③ In addition, as an alternative to GMRES(m), LGMRES makes JFNK more efficient.

Key words: negative-flux fixup, k-eigenvalue, nonlinear transport, discrete ordinates, JFNK

CLC Number:

TL323

Kaibo ZHU, Longfei XU, Liujun PAN, Huayun SHEN. Application of JFNK Method in S_N Transport Calculations[J]. Chinese Journal of Computational Physics, 2021, 38(4): 381-392.

Figures/Tables 16

References 16

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区域	Σ_t	Σ_S	Q
(I)	1.0	1.0	1.0
(II)	0.001	0.0	0.0
(III)	100.0	0.0	0.0
(IV)	10.0	9.999	0.0

区域	Σ_t	Σ_S	Q
(I)	1.0	1.0	1.0
(II)	0.001	0.0	0.0
(III)	100.0	0.0	0.0
(IV)	10.0	9.999	0.0

方法	误差	迭代次数	扫描次数	时间/s
SI	9.30×10^-6	160	160	10.395
GMRES	5.39×10^-6	14	18	1.207
JFNK	6.28×10^-6	(17)	22	1.404

方法	误差	迭代次数	扫描次数	时间/s
SI	9.30×10^-6	160	160	10.395
GMRES	5.39×10^-6	14	18	1.207
JFNK	6.28×10^-6	(17)	22	1.404

方法	误差	迭代次数	扫描次数	时间/s
SI	9.60×10^-6	158	158	12.744
JFNK(η₁)	6.43×10^-7	(6，8，15，16)	55	4.665
JFNK(η₂)	6.23×10^-8	(16，19，18)	61	5.094