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Title: A multi-group extended linear discontinuous method for fixed-source discrete ordinates problems in slab geometry

Authors: Iram B. Rivas-Ortiz; Dany S. Dominguez; Carlos R. García Hernández; Susana M. Iglesias

Addresses: Instituto Superior de Tecnologías y Ciencias Aplicadas, Universidad de la Habana, Quinta de los Molinos, Ave. Salvador Allende 1100, e/Infanta y Rancho Boyeros, Vedado, La Habana, Cuba ' Pós-graduação em Modelagem Computacional, Universidade Estadual de Santa Cruz, Rodovia Jorge Amado, km 16, Salobrinho, 45662-900 Ilhéus, BA, Brazil ' Instituto Superior de Tecnologías y Ciencias Aplicadas, Universidad de la Habana, Quinta de los Molinos, Ave. Salvador Allende 1100, e/ Infanta y Rancho Boyeros, Vedado, La Habana, Cuba ' Pós-graduação em Modelagem Computacional, Universidade Estadual de Santa Cruz, Rodovia Jorge Amado, km 16, Salobrinho, 45662-900 Ilhéus, BA, Brazil

Abstract: At present, neutron density calculation in non-multiplying media is relevant in many areas of engineering and science. In this paper, we propose the Extended Linear Discontinuous (ELD) method in multi-group discrete ordinates formulation, originally formulated for one-energy group fixed-source problems with isotropic scattering source in slab geometry. The proposed auxiliary equations are uncoupled on angular directions and combine the linear discontinuous approximation of the finite element method and the quasi-analytical general solution of the spectral nodal method. Thus, we can implement an efficient and simple algorithm using the conventional source iteration scheme for the sweeping equations. Numerical results for benchmark problems are presented to illustrate the accuracy and computational performance of the ELD method. The work shows that the main advantages of the proposed method are that the numerical scheme is stable for coarse-meshes, and its numerical results are more accurate than those generated by the Diamond Difference (DD) and Linear Discontinuous (LD) methods.

Keywords: multi-group transport problems; discrete ordinate formulation; fixed-source problems; linear discontinuous.

DOI: 10.1504/IJNEST.2019.099721

International Journal of Nuclear Energy Science and Technology, 2019 Vol.13 No.1, pp.70 - 86

Received: 26 Nov 2018
Accepted: 15 Mar 2019

Published online: 26 Apr 2019 *

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