Unstructured Grids and the Multigroup Neutron Diffusion Equation
The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term usin...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Science and Technology of Nuclear Installations |
| Online Access: | http://dx.doi.org/10.1155/2013/641863 |
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| author | German Theler |
| author_facet | German Theler |
| author_sort | German Theler |
| collection | DOAJ |
| description | The neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. This work introduces the alternatives that unstructured grids can provide to aid the engineers to solve the neutron diffusion problem and gives a brief overview of the variety of possibilities they offer. It is by understanding the basic mathematics that lie beneath the equations that model real physical systems; better technical decisions can be made. It is in this spirit that this paper is written, giving a first introduction to the basic concepts which can be incorporated into core-level neutron flux computations. A simple two-dimensional homogeneous circular reactor is solved using a coarse unstructured grid in order to illustrate some basic differences between the finite volumes and the finite elements method. Also, the classic 2D IAEA PWR benchmark problem is solved for eighty combinations of symmetries, meshing algorithms, basic geometric entities, discretization schemes, and characteristic grid lengths, giving even more insight into the peculiarities that arise when solving the neutron diffusion equation using unstructured grids. |
| format | Article |
| id | doaj-art-2a0c90250b8d4fbbbfa7ab3b370a93e3 |
| institution | Kabale University |
| issn | 1687-6075 1687-6083 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Science and Technology of Nuclear Installations |
| spelling | doaj-art-2a0c90250b8d4fbbbfa7ab3b370a93e32025-02-03T06:12:39ZengWileyScience and Technology of Nuclear Installations1687-60751687-60832013-01-01201310.1155/2013/641863641863Unstructured Grids and the Multigroup Neutron Diffusion EquationGerman Theler0TECNA Estudios y Proyectos de Ingeniería S.A., Encarnación Ezcurra 365, C1107CLA Buenos Aires, ArgentinaThe neutron diffusion equation is often used to perform core-level neutronic calculations. It consists of a set of second-order partial differential equations over the spatial coordinates that are, both in the academia and in the industry, usually solved by discretizing the neutron leakage term using a structured grid. This work introduces the alternatives that unstructured grids can provide to aid the engineers to solve the neutron diffusion problem and gives a brief overview of the variety of possibilities they offer. It is by understanding the basic mathematics that lie beneath the equations that model real physical systems; better technical decisions can be made. It is in this spirit that this paper is written, giving a first introduction to the basic concepts which can be incorporated into core-level neutron flux computations. A simple two-dimensional homogeneous circular reactor is solved using a coarse unstructured grid in order to illustrate some basic differences between the finite volumes and the finite elements method. Also, the classic 2D IAEA PWR benchmark problem is solved for eighty combinations of symmetries, meshing algorithms, basic geometric entities, discretization schemes, and characteristic grid lengths, giving even more insight into the peculiarities that arise when solving the neutron diffusion equation using unstructured grids.http://dx.doi.org/10.1155/2013/641863 |
| spellingShingle | German Theler Unstructured Grids and the Multigroup Neutron Diffusion Equation Science and Technology of Nuclear Installations |
| title | Unstructured Grids and the Multigroup Neutron Diffusion Equation |
| title_full | Unstructured Grids and the Multigroup Neutron Diffusion Equation |
| title_fullStr | Unstructured Grids and the Multigroup Neutron Diffusion Equation |
| title_full_unstemmed | Unstructured Grids and the Multigroup Neutron Diffusion Equation |
| title_short | Unstructured Grids and the Multigroup Neutron Diffusion Equation |
| title_sort | unstructured grids and the multigroup neutron diffusion equation |
| url | http://dx.doi.org/10.1155/2013/641863 |
| work_keys_str_mv | AT germantheler unstructuredgridsandthemultigroupneutrondiffusionequation |