Time-dependent simplified spherical harmonics formulations for a nuclear reactor system
The steady-state simplified spherical harmonics equations (SPN equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by compari...
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doaj-dd79a13eb05447c384eb56137c4f57612021-09-17T04:34:24ZengElsevierNuclear Engineering and Technology1738-57332021-12-01531238613878Time-dependent simplified spherical harmonics formulations for a nuclear reactor systemA. Carreño0A. Vidal-Ferràndiz1D. Ginestar2G. Verdú3Instituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental, Universitat Politècnica de València, Camino de Vera, s/n, 46022, València, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022, València, SpainInstituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022, València, SpainInstituto Universitario de Seguridad Industrial, Radiofísica y Medioambiental, Universitat Politècnica de València, Camino de Vera, s/n, 46022, València, Spain; Corresponding author.The steady-state simplified spherical harmonics equations (SPN equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SPN equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.http://www.sciencedirect.com/science/article/pii/S1738573321003314Implified spherical harmonic equationsFinite element methodTime-dependent neutron transport approximations |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
A. Carreño A. Vidal-Ferràndiz D. Ginestar G. Verdú |
spellingShingle |
A. Carreño A. Vidal-Ferràndiz D. Ginestar G. Verdú Time-dependent simplified spherical harmonics formulations for a nuclear reactor system Nuclear Engineering and Technology Implified spherical harmonic equations Finite element method Time-dependent neutron transport approximations |
author_facet |
A. Carreño A. Vidal-Ferràndiz D. Ginestar G. Verdú |
author_sort |
A. Carreño |
title |
Time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
title_short |
Time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
title_full |
Time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
title_fullStr |
Time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
title_full_unstemmed |
Time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
title_sort |
time-dependent simplified spherical harmonics formulations for a nuclear reactor system |
publisher |
Elsevier |
series |
Nuclear Engineering and Technology |
issn |
1738-5733 |
publishDate |
2021-12-01 |
description |
The steady-state simplified spherical harmonics equations (SPN equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SPN equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system. |
topic |
Implified spherical harmonic equations Finite element method Time-dependent neutron transport approximations |
url |
http://www.sciencedirect.com/science/article/pii/S1738573321003314 |
work_keys_str_mv |
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