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

Authors:
ORCiD logo; ORCiD logo;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1397805
Grant/Contract Number:
AC05-00OR22725
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 345; Journal Issue: C; Related Information: CHORUS Timestamp: 2017-10-04 22:13:28; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English

Citation Formats

Kochunas, Brendan, Fitzgerald, Andrew, and Larsen, Edward. Fourier analysis of iteration schemes for k -eigenvalue transport problems with flux-dependent cross sections. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.05.028.
Kochunas, Brendan, Fitzgerald, Andrew, & Larsen, Edward. Fourier analysis of iteration schemes for k -eigenvalue transport problems with flux-dependent cross sections. United States. doi:10.1016/j.jcp.2017.05.028.
Kochunas, Brendan, Fitzgerald, Andrew, and Larsen, Edward. 2017. "Fourier analysis of iteration schemes for k -eigenvalue transport problems with flux-dependent cross sections". United States. doi:10.1016/j.jcp.2017.05.028.
@article{osti_1397805,
title = {Fourier analysis of iteration schemes for k -eigenvalue transport problems with flux-dependent cross sections},
author = {Kochunas, Brendan and Fitzgerald, Andrew and Larsen, Edward},
abstractNote = {},
doi = {10.1016/j.jcp.2017.05.028},
journal = {Journal of Computational Physics},
number = C,
volume = 345,
place = {United States},
year = 2017,
month = 9
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on May 30, 2018
Publisher's Accepted Manuscript

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  • Often in reactor dynamics, higher eigenfunctions of the multigroup diffusion equation must be determined. An algorithm to calculate higher eigenfunctions (modes) of the [lambda]-eigenvalue problem corresponding to the steady-state two-group neutron diffusion equation is presented. The method is based on a special type of subspace iteration for large sparse nonsymmetric eigenvalue problems. Having been tested using an International Atomic Energy Agency benchmark problem and also applied to a VVER-1000 pressurized water reactor assembly, the algorithm was found to work very effectively and reliably. In its application, the algorithm presented is not restricted to the [lambda]-eigenvalue problem only but is alsomore » generally applicable to large sparse nonsymmetric eigenvalue problems even with multiple and complex eigenvalues.« less
  • In this article, the quasi-Laguerre iteration is established in the spirit of Laguerre`s iteration for solving polynomial f with all real zeros. The new algorithm, which maintains the monotonicity and global convergence of the Laguerre iteration, no longer needs to evaluate f{double_prime}. The ultimate convergence rate is {radical}2 + 1. When applied to approximate the eigenvalues of a symmetric tridiagonal matrix, the algorithm substantially improves the speed of Laguerre`s iteration.
  • Two versions of flux corrected transport and two versions of total variation diminishing schemes are tested for several one- and two-dimensional hydrodynamic and magnetohydrodynamic problems. Two of the schemes, YDFCT and TVDLF are tested extensively for the first time. The results give an insight into the limitations of the methods, their relative strengths and weaknesses. Some subtle points of the algorithms and the effects of selecting different options for certain methods are emphasised. 38 refs., 9 figs., 1 tab.