Application of the piecewise constant function approximation method to modified point kinetics

Bruno Nascimento Martins; Alessandro da Cruz Gonçalves; Zelmo  Rodrigues de Lima

doi:10.15392/2319-0612.2024.2588

Authors

Bruno Nascimento Martins Eletronuclear https://orcid.org/0009-0008-0707-7648
Alessandro da Cruz Gonçalves Universidade Federal do Rio de Janeiro, PEN/COPPE
Zelmo Rodrigues de Lima Instituto de Engenharia Nuclear

DOI:

https://doi.org/10.15392/2319-0612.2024.2588

Keywords:

reactivity, point kinetics, PCA, relaxation time

Abstract

This work uses the numerical method known as Piecewise Constant Approximation, PCA, to solve the equations of modified point kinetics for six groups of delayed neutron precursors. The modified point kinetics corresponds to the point kinetics model without considering the approximation for the derivative of the logarithm of the neutron current. Applying the PCA method approximates the reactivity function to continuous piecewise functions, and the resulting system of first-order differential equations can be solved exactly in each time partition. For validation, numerical simulations are carried out for the cases of constant reactivity, step type and time-varying reactivity, ramp type, and the results are compared with those obtained by the finite difference method. Quantitative analysis of the results shows that the PCA method can efficiently obtain good results for modified point kinetics.

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