Using Generalized Basis for Functional Expansion
Functional expansion has been rigorously studied as a promising method in stochastic neutron transport and multi-physics coupling. It is a method to represent data specified on a desired domain as an expansion of basis set in a continuous manner. For convenience, the basis set for functional expansi...
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| Format: | Article |
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Multidisciplinary Digital Publishing Institute
2021
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| Online Access: | https://hdl.handle.net/1721.1/133193 |
| _version_ | 1811087105176109056 |
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| author | Han, Zhuoran Forget, Benoit Smith, Kord |
| author_facet | Han, Zhuoran Forget, Benoit Smith, Kord |
| author_sort | Han, Zhuoran |
| collection | MIT |
| description | Functional expansion has been rigorously studied as a promising method in stochastic neutron transport and multi-physics coupling. It is a method to represent data specified on a desired domain as an expansion of basis set in a continuous manner. For convenience, the basis set for functional expansion is typically chosen to be orthogonal. In cylindrical PWR pin-cell simulations, the orthogonal Zernike polynomials have been used. The main advantage of using functional expansion in nuclear modeling is that it requires less memory to represent temperature and nuclide variations in fuel then using a fine discretization. Fewer variables are involved in the data storage and transfer process. Each nuclide can have its unique expansion order, which becomes very important for depletion problems. In a recent study, performance analysis was conducted on Zernike-based FETs on a 2D PWR geometry. For reaction rates like the absorption rate of U-238, however, many orders are needed with Zernike-based FETs to achieve a reasonable accuracy. This gap inspires the study in this paper on alternative basis set that can better capture the steep gradient with fewer orders. In this paper, a generalized functional expansion method is established. The basis set can be an arbitrary series of independent functions. To capture the self-shielding effect of U-238 absorption rate, an exponential basis set is chosen. The results show that the expansion order utilizing exponential basis can reduce by half of that from using orthogonal Zernike polynomials while achieving the same accuracy. The integrated reaction rate is also demonstrated to be preserved. This paper also shows that the generalized functional expansion could be a heuristic method for further investigation on continuous depletion problems. |
| first_indexed | 2024-09-23T13:39:49Z |
| format | Article |
| id | mit-1721.1/133193 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T13:39:49Z |
| publishDate | 2021 |
| publisher | Multidisciplinary Digital Publishing Institute |
| record_format | dspace |
| spelling | mit-1721.1/1331932021-11-01T14:36:55Z Using Generalized Basis for Functional Expansion Han, Zhuoran Forget, Benoit Smith, Kord Functional expansion has been rigorously studied as a promising method in stochastic neutron transport and multi-physics coupling. It is a method to represent data specified on a desired domain as an expansion of basis set in a continuous manner. For convenience, the basis set for functional expansion is typically chosen to be orthogonal. In cylindrical PWR pin-cell simulations, the orthogonal Zernike polynomials have been used. The main advantage of using functional expansion in nuclear modeling is that it requires less memory to represent temperature and nuclide variations in fuel then using a fine discretization. Fewer variables are involved in the data storage and transfer process. Each nuclide can have its unique expansion order, which becomes very important for depletion problems. In a recent study, performance analysis was conducted on Zernike-based FETs on a 2D PWR geometry. For reaction rates like the absorption rate of U-238, however, many orders are needed with Zernike-based FETs to achieve a reasonable accuracy. This gap inspires the study in this paper on alternative basis set that can better capture the steep gradient with fewer orders. In this paper, a generalized functional expansion method is established. The basis set can be an arbitrary series of independent functions. To capture the self-shielding effect of U-238 absorption rate, an exponential basis set is chosen. The results show that the expansion order utilizing exponential basis can reduce by half of that from using orthogonal Zernike polynomials while achieving the same accuracy. The integrated reaction rate is also demonstrated to be preserved. This paper also shows that the generalized functional expansion could be a heuristic method for further investigation on continuous depletion problems. 2021-10-27T18:07:29Z 2021-10-27T18:07:29Z 2021-04-29 2021-05-13T14:34:18Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/133193 Journal of Nuclear Engineering 2 (2): 161-167 (2021) PUBLISHER_CC http://dx.doi.org/10.3390/jne2020016 Creative Commons Attribution https://creativecommons.org/licenses/by/4.0/ application/pdf Multidisciplinary Digital Publishing Institute Multidisciplinary Digital Publishing Institute |
| spellingShingle | Han, Zhuoran Forget, Benoit Smith, Kord Using Generalized Basis for Functional Expansion |
| title | Using Generalized Basis for Functional Expansion |
| title_full | Using Generalized Basis for Functional Expansion |
| title_fullStr | Using Generalized Basis for Functional Expansion |
| title_full_unstemmed | Using Generalized Basis for Functional Expansion |
| title_short | Using Generalized Basis for Functional Expansion |
| title_sort | using generalized basis for functional expansion |
| url | https://hdl.handle.net/1721.1/133193 |
| work_keys_str_mv | AT hanzhuoran usinggeneralizedbasisforfunctionalexpansion AT forgetbenoit usinggeneralizedbasisforfunctionalexpansion AT smithkord usinggeneralizedbasisforfunctionalexpansion |