On the stability of the Discrete Generalized Multigroup method
This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed g...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2017
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| Online Access: | http://hdl.handle.net/1721.1/108026 https://orcid.org/0000-0001-7717-0364 https://orcid.org/0000-0003-1459-7672 |
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| author | Gibson, Nathan A. Forget, Benoit Gibson, Nathan Andrew Forget, Benoit Robert Yves |
| author2 | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Gibson, Nathan A. Forget, Benoit Gibson, Nathan Andrew Forget, Benoit Robert Yves |
| author_sort | Gibson, Nathan A. |
| collection | MIT |
| description | This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed group mapping scheme. This work presents a mapping procedure that improves stability of the original method for fine group calculations. Additionally, a relaxation scheme, Krasnoselskij iteration, is introduced to the fixed point iteration to further improve the stability characteristics and remove the need for fine group flux updates. Both improvements are applied on heterogeneous problems using the SHEM361 and the NG2042 group structures. The results indicate improved stability from a well-informed group mapping and demonstrate the possibility of eliminating the need for fine group flux updates. |
| first_indexed | 2024-09-23T09:05:12Z |
| format | Article |
| id | mit-1721.1/108026 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:05:12Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/1080262022-09-26T10:21:13Z On the stability of the Discrete Generalized Multigroup method Gibson, Nathan A. Forget, Benoit Gibson, Nathan Andrew Forget, Benoit Robert Yves Massachusetts Institute of Technology. Department of Nuclear Science and Engineering Forget, Benoit Robert Yves Gibson, Nathan Andrew Forget, Benoit Robert Yves This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed group mapping scheme. This work presents a mapping procedure that improves stability of the original method for fine group calculations. Additionally, a relaxation scheme, Krasnoselskij iteration, is introduced to the fixed point iteration to further improve the stability characteristics and remove the need for fine group flux updates. Both improvements are applied on heterogeneous problems using the SHEM361 and the NG2042 group structures. The results indicate improved stability from a well-informed group mapping and demonstrate the possibility of eliminating the need for fine group flux updates. United States. Dept. of Energy. Naval Reactors Division 2017-04-10T19:32:03Z 2017-04-10T19:32:03Z 2014-01 2013-11 Article http://purl.org/eprint/type/JournalArticle 0306-4549 http://hdl.handle.net/1721.1/108026 Gibson, Nathan A., and Forget, Benoit. “On the Stability of the Discrete Generalized Multigroup Method.” Annals of Nuclear Energy 65 (March 2014): 421–432. © 2013 Elsevier Ltd https://orcid.org/0000-0001-7717-0364 https://orcid.org/0000-0003-1459-7672 en_US http://dx.doi.org/10.1016/j.anucene.2013.11.032 Annals of Nuclear Energy Creative Commons Attribution-NonCommercial-NoDerivs License http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier Prof. Forget via Chris Sherratt |
| spellingShingle | Gibson, Nathan A. Forget, Benoit Gibson, Nathan Andrew Forget, Benoit Robert Yves On the stability of the Discrete Generalized Multigroup method |
| title | On the stability of the Discrete Generalized Multigroup method |
| title_full | On the stability of the Discrete Generalized Multigroup method |
| title_fullStr | On the stability of the Discrete Generalized Multigroup method |
| title_full_unstemmed | On the stability of the Discrete Generalized Multigroup method |
| title_short | On the stability of the Discrete Generalized Multigroup method |
| title_sort | on the stability of the discrete generalized multigroup method |
| url | http://hdl.handle.net/1721.1/108026 https://orcid.org/0000-0001-7717-0364 https://orcid.org/0000-0003-1459-7672 |
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