Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method
In this work, we used a modified Picard’s method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calcula...
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Brazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR)
2021-07-01
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| Series: | Brazilian Journal of Radiation Sciences |
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| Online Access: | https://bjrs.org.br/revista/index.php/REVISTA/article/view/731 |
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| author | Matheus Gularte Tavares Claudio Zen Petersen Marcelo Schramm Rodrigo Zanette |
| author_facet | Matheus Gularte Tavares Claudio Zen Petersen Marcelo Schramm Rodrigo Zanette |
| author_sort | Matheus Gularte Tavares |
| collection | DOAJ |
| description | In this work, we used a modified Picard’s method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a first order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform by Stehfest method. We present numerical simulations and comparisons with available results in literature. |
| format | Article |
| id | doaj-art-c3e4f7cca2c847ef91d190a840faeb0b |
| institution | Kabale University |
| issn | 2319-0612 |
| language | English |
| publishDate | 2021-07-01 |
| publisher | Brazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR) |
| record_format | Article |
| series | Brazilian Journal of Radiation Sciences |
| spelling | doaj-art-c3e4f7cca2c847ef91d190a840faeb0b2025-08-20T03:50:49ZengBrazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR)Brazilian Journal of Radiation Sciences2319-06122021-07-0192A (Suppl.)10.15392/bjrs.v9i2A.731570Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative MethodMatheus Gularte Tavares0Claudio Zen PetersenMarcelo SchrammRodrigo ZanetteFederal University of PelotasIn this work, we used a modified Picard’s method to solve the Multigroup Neutron Space Kinetics Equations (MNSKE) in Cartesian geometry. The method consists in assuming an initial guess for the neutron flux and using it to calculate a fictitious source term in the MNSKE. A new source term is calculated applying its solution, and so on, iteratively, until a stop criterion is satisfied. For the solution of the fast and thermal neutron fluxes equations, the Laplace Transform technique is used in time variable resulting in a first order linear differential matrix equation, which are solved by classical methods in the literature. After each iteration, the scalar neutron flux and the delayed neutron precursors are reconstructed by polynomial interpolation. We obtain the fluxes and precursors through Numerical Inverse Laplace Transform by Stehfest method. We present numerical simulations and comparisons with available results in literature.https://bjrs.org.br/revista/index.php/REVISTA/article/view/731neutron diffusion equationsource iterative methodlaplace transformstehfest algorithmpolinomial interpola-tion. |
| spellingShingle | Matheus Gularte Tavares Claudio Zen Petersen Marcelo Schramm Rodrigo Zanette Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method Brazilian Journal of Radiation Sciences neutron diffusion equation source iterative method laplace transform stehfest algorithm polinomial interpola-tion. |
| title | Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method |
| title_full | Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method |
| title_fullStr | Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method |
| title_full_unstemmed | Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method |
| title_short | Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method |
| title_sort | solution for the multigroup neutron space kinetics equations by source iterative method |
| topic | neutron diffusion equation source iterative method laplace transform stehfest algorithm polinomial interpola-tion. |
| url | https://bjrs.org.br/revista/index.php/REVISTA/article/view/731 |
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