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http://dx.doi.org/10.1016/j.net.2021.06.010

Time-dependent simplified spherical harmonics formulations for a nuclear reactor system  

Carreno, A. (Instituto Universitario de Seguridad Industrial, Radiofisica y Medioambiental, Universitat Politecnica de Valencia)
Vidal-Ferrandiz, A. (Instituto Universitario de Matematica Multidisciplinar, Universitat Politecnica de Valencia)
Ginestar, D. (Instituto Universitario de Matematica Multidisciplinar, Universitat Politecnica de Valencia)
Verdu, G. (Instituto Universitario de Seguridad Industrial, Radiofisica y Medioambiental, Universitat Politecnica de Valencia)
Publication Information
Nuclear Engineering and Technology / v.53, no.12, 2021 , pp. 3861-3878 More about this Journal
Abstract
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.
Keywords
Implified spherical harmonic equations; Finite element method; Time-dependent neutron transport; approximations;
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