Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4967407 | Journal of Computational Physics | 2017 | 26 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Brendan Kochunas, Andrew Fitzgerald, Edward Larsen,