Fourier analysis of iteration schemes for k-eigenvalue transport problems with flux-dependent cross sections

JOURNAL OF COMPUTATIONAL PHYSICS

卷:345

Article

Kochunas, Brendan¹  Fitzgerald, Andrew¹  Larsen, Edward¹ 

[1] Univ Michigan, Dept Nucl Engn & Radiol Sci, Ann Arbor, MI 48109 USA

关键词: Fourier analysis;    Coupled physics;    Neutron transport;    Iterative convergence;   

DOI  :  10.1016/j.jcp.2017.05.028

来源: Elsevier

【 摘 要 】

A central problem in nuclear reactor analysis is calculating solutions of steady-state k-eigenvalue problems with thermal hydraulic feedback. In this paper we propose and utilize a model problem that permits the theoretical analysis of iterative schemes for solving such problems. To begin, we discuss a model problem (with nonlinear cross section feedback) and its justification. We proceed with a Fourier analysis for source iteration schemes applied to the model problem. Then we analyze commonly-used iteration schemes involving non-linear diffusion acceleration and feedback. For each scheme we show (1) that they are conditionally stable, (2) the conditions that lead to instability, and (3) that traditional relaxation approaches can improve stability. Lastly, we propose a new iteration scheme that theory predicts is an improvement upon the existing methods. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free