Open AccessSolution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method
Author(s) -
Matheus Gularte Tavares
Publication year - 2021
Publication title -
brazilian journal of radiation sciences
Language(s) - English
Resource type - Journals
ISSN - 2319-0612
DOI - 10.15392/bjrs.v9i2a.731
Subject(s) - laplace transform , mathematical analysis , mathematics , inverse laplace transform , differential equation , scalar (mathematics) , neutron , polynomial interpolation , laplace's equation , interpolation (computer graphics) , iterative method , polynomial , physics , linear interpolation , mathematical optimization , geometry , classical mechanics , nuclear physics , motion (physics)
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.