Solution for the Multigroup Neutron Space Kinetics Equations by Source Iterative Method
DOI:
https://doi.org/10.15392/bjrs.v9i2A.731Palabras clave:
Neutron Diffusion Equation, Source Iterative Method, Laplace Transform, Stehfest Algorithm, Polinomial Interpola-tion.Resumen
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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WILLERT, J.; TAITANO, T; KNOLL, D. Leveraging anderson acceleration for improved conver-gence of iterative solutions to transport systems. Journal of Computational Physics, v. 273, p. 122-132, 2014. DOI: https://doi.org/10.1016/j.jcp.2014.05.015
ADAMS, M.; LARSEN, E. Fast iterative methods for discrete ordinates particle transport calcula-tions. Progress in Nuclear Energy, v. 40, p. 3-159, 2002. DOI: https://doi.org/10.1016/S0149-1970(01)00023-3
DANIELLA, M. Métodos de Aceleração para a Solução da Equação de Transporte. 2017. Tese de Doutorado - PPGMAP/UFRGS, Porto Alegre/RS.
ZANETTE, R. Solução da Equação de Difusão de Nêutrons Multigrupo Multirregião Estacionária em Geometria Cartesiana pelo Método da Potência via Fronteiras Fictícias. 2017. Dissertação de Mestrado - PPGMAT/UFPEL, Pelotas/RS. DOI: https://doi.org/10.5540/03.2017.005.01.0390
NAHLA, A.; et al. Numerical Techniques for the Neutron Diffusion Equations in the Nuclear Reac-tors. Adv. Studies Theor. Physics, v. 6, p.649-664, 2012.
CEOLIN, C.; et al. On the analytical Solution of the multi group neutron diffusion kinetic equation in a multlayered slab. International Nuclear Atlantic Conference, 2011, Belo Horizonte, MG, Bra-zil, October 24 to October 28 (2011).
CORNO, S. et al. Analytical approach to the neutron kinetics of the non-homogeneous reactor. Progress in Nuclear Energy, v. 50, p. 847-865, 2008. DOI: https://doi.org/10.1016/j.pnucene.2008.02.001
HASSANZADEH, H.; POOLDADI-DARVISH, M. Comparison of different numerical Laplace inversion methods for engineering applications. Applied mathematics and computation, v. 189, p. 1966-1981, 2007. DOI: https://doi.org/10.1016/j.amc.2006.12.072
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Derechos de autor 2021 Brazilian Journal of Radiation Sciences (BJRS)
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