Variational nodal methods for neutron transport: 40 years in review
The variational nodal method for solving the neutron transport equation has evolved over 40 years. Based on a functional form of the Boltzmann neutron transport equation, the method now comprises a complete set of variants that can be employed for different problems. This paper presents an extensive...
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| Format: | Article |
| Language: | English |
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Elsevier
2022-09-01
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| Series: | Nuclear Engineering and Technology |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S1738573322002157 |
| _version_ | 1811281177797984256 |
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| author | Tengfei Zhang Zhipeng Li |
| author_facet | Tengfei Zhang Zhipeng Li |
| author_sort | Tengfei Zhang |
| collection | DOAJ |
| description | The variational nodal method for solving the neutron transport equation has evolved over 40 years. Based on a functional form of the Boltzmann neutron transport equation, the method now comprises a complete set of variants that can be employed for different problems. This paper presents an extensive review of the development of the variational nodal method. The emphasis is on summarizing the whole theoretical system rather than validating the methodologies. The paper covers the variational nodal formulation of the Boltzmann neutron transport equation, the Ritz procedure for various application purposes, the derivation of boundary conditions, the extension for adjoint and perturbation calculations, and treatments for anisotropic scattering sources. Acceleration approaches for constructing response matrices and solving the resulting system of algebraic equations are also presented. |
| first_indexed | 2024-04-13T01:28:48Z |
| format | Article |
| id | doaj.art-afdd480c16784b72bf9201432ecf48fd |
| institution | Directory Open Access Journal |
| issn | 1738-5733 |
| language | English |
| last_indexed | 2024-04-13T01:28:48Z |
| publishDate | 2022-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Engineering and Technology |
| spelling | doaj.art-afdd480c16784b72bf9201432ecf48fd2022-12-22T03:08:34ZengElsevierNuclear Engineering and Technology1738-57332022-09-0154931813204Variational nodal methods for neutron transport: 40 years in reviewTengfei Zhang0Zhipeng Li1School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai, China; Corresponding author.CAEP Software Centre for High Performance Numerical Simulation, Beijing, China; Innstitute of Applied Physics and Computational Mathematics, Beijing, ChinaThe variational nodal method for solving the neutron transport equation has evolved over 40 years. Based on a functional form of the Boltzmann neutron transport equation, the method now comprises a complete set of variants that can be employed for different problems. This paper presents an extensive review of the development of the variational nodal method. The emphasis is on summarizing the whole theoretical system rather than validating the methodologies. The paper covers the variational nodal formulation of the Boltzmann neutron transport equation, the Ritz procedure for various application purposes, the derivation of boundary conditions, the extension for adjoint and perturbation calculations, and treatments for anisotropic scattering sources. Acceleration approaches for constructing response matrices and solving the resulting system of algebraic equations are also presented.http://www.sciencedirect.com/science/article/pii/S1738573322002157Variational nodal methodNeutron transport equation |
| spellingShingle | Tengfei Zhang Zhipeng Li Variational nodal methods for neutron transport: 40 years in review Nuclear Engineering and Technology Variational nodal method Neutron transport equation |
| title | Variational nodal methods for neutron transport: 40 years in review |
| title_full | Variational nodal methods for neutron transport: 40 years in review |
| title_fullStr | Variational nodal methods for neutron transport: 40 years in review |
| title_full_unstemmed | Variational nodal methods for neutron transport: 40 years in review |
| title_short | Variational nodal methods for neutron transport: 40 years in review |
| title_sort | variational nodal methods for neutron transport 40 years in review |
| topic | Variational nodal method Neutron transport equation |
| url | http://www.sciencedirect.com/science/article/pii/S1738573322002157 |
| work_keys_str_mv | AT tengfeizhang variationalnodalmethodsforneutrontransport40yearsinreview AT zhipengli variationalnodalmethodsforneutrontransport40yearsinreview |