Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method
Many numerical methods are being used to solve the multigroup neutron diffusion equation for different types of nuclear reactors. These methods solve this equation quite accurately and determine the neutron flux and power distribution in the reactor as well as the eigenvalue of the reactor core. In...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Brazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR)
2022-10-01
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| Series: | Brazilian Journal of Radiation Sciences |
| Subjects: | |
| Online Access: | https://bjrs.org.br/revista/index.php/REVISTA/article/view/2005 |
| _version_ | 1797991851331944448 |
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| author | Adilson Costa da Silva Aquilino Martinez Rodrigo Diniz Alessandro Gonçalves |
| author_facet | Adilson Costa da Silva Aquilino Martinez Rodrigo Diniz Alessandro Gonçalves |
| author_sort | Adilson Costa da Silva |
| collection | DOAJ |
| description |
Many numerical methods are being used to solve the multigroup neutron diffusion equation for different types of nuclear reactors. These methods solve this equation quite accurately and determine the neutron flux and power distribution in the reactor as well as the eigenvalue of the reactor core. In this paper, we are proposing the integration of an analytical solution with an iterative method to determine the neutron flux distribution in the reactor and the effective eigenvalue. To do this, we solve the one-dimensional neutron diffusion equation for two energy groups, where the nuclear parameters are uniform in both nuclear fuel and reflector regions. The eigenvalue will be determined from the analytical solution using the power method iteratively until reaching convergence in both flux and eigenvalue. The results obtained in this paper are compared with results obtained from numerical methods used to validate the proposed method.
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| first_indexed | 2024-04-11T08:58:41Z |
| format | Article |
| id | doaj.art-b428546be59e41d3a7305483fa7c2f4e |
| institution | Directory Open Access Journal |
| issn | 2319-0612 |
| language | English |
| last_indexed | 2024-04-11T08:58:41Z |
| publishDate | 2022-10-01 |
| publisher | Brazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR) |
| record_format | Article |
| series | Brazilian Journal of Radiation Sciences |
| spelling | doaj.art-b428546be59e41d3a7305483fa7c2f4e2022-12-22T04:33:08ZengBrazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR)Brazilian Journal of Radiation Sciences2319-06122022-10-01103A10.15392/2319-0612.2022.2005Analytical solution of the multigroup neutron diffusion equation coupled with an iterative methodAdilson Costa da Silva0Aquilino MartinezRodrigo DinizAlessandro GonçalvesUniversidade Federal do Rio de Janeiro - UFRJ Many numerical methods are being used to solve the multigroup neutron diffusion equation for different types of nuclear reactors. These methods solve this equation quite accurately and determine the neutron flux and power distribution in the reactor as well as the eigenvalue of the reactor core. In this paper, we are proposing the integration of an analytical solution with an iterative method to determine the neutron flux distribution in the reactor and the effective eigenvalue. To do this, we solve the one-dimensional neutron diffusion equation for two energy groups, where the nuclear parameters are uniform in both nuclear fuel and reflector regions. The eigenvalue will be determined from the analytical solution using the power method iteratively until reaching convergence in both flux and eigenvalue. The results obtained in this paper are compared with results obtained from numerical methods used to validate the proposed method. https://bjrs.org.br/revista/index.php/REVISTA/article/view/2005Neutron diffusion equationanalytical solutioniterative methodeigenvalueslab reactor |
| spellingShingle | Adilson Costa da Silva Aquilino Martinez Rodrigo Diniz Alessandro Gonçalves Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method Brazilian Journal of Radiation Sciences Neutron diffusion equation analytical solution iterative method eigenvalue slab reactor |
| title | Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| title_full | Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| title_fullStr | Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| title_full_unstemmed | Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| title_short | Analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| title_sort | analytical solution of the multigroup neutron diffusion equation coupled with an iterative method |
| topic | Neutron diffusion equation analytical solution iterative method eigenvalue slab reactor |
| url | https://bjrs.org.br/revista/index.php/REVISTA/article/view/2005 |
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