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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Main Authors: Matheus Gularte Tavares, Claudio Zen Petersen, Marcelo Schramm, Rodrigo Zanette
Format: Article
Language:English
Published: Brazilian Radiation Protection Society (Sociedade Brasileira de Proteção Radiológica, SBPR) 2021-07-01
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.
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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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AT claudiozenpetersen solutionforthemultigroupneutronspacekineticsequationsbysourceiterativemethod
AT marceloschramm solutionforthemultigroupneutronspacekineticsequationsbysourceiterativemethod
AT rodrigozanette solutionforthemultigroupneutronspacekineticsequationsbysourceiterativemethod