The spectral nodal method applied to multigroup <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>S</mml:mi><mml:mi>N</mml:mi></mml:msub></mml:mrow></mml:math> neutron transport problems in One-Dimensional geometry with Fixed–Source

Oliva, Amaury Muñoz; Filho, Hermes Alves; Silva, Davi José Martins e; Hernández, Carlos Rafael García

doi:10.1016/j.pnucene.2017.12.017

Cited by 13 publications

(15 citation statements)

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“…In this section, the Spectral Deterministic Method (SDM) (OLIVA et al, 2016;OLIVA et al, 2018) and the iterative procedure to solve the neutron transport equation using the SDM method for heterogeneous problems is presented. Let us consider the heterogeneous slab represented in Fig.…”

Section: The Multigroup Spectral Deterministic Method(sdm) For Hetementioning

confidence: 99%

“…In an earlier paper (OLIVA et al, 2016;OLIVA et al, 2018), a numerical method was proposed for obtaining numerical solutions free from spatial truncation errors for all spatial cell sizes, one group and multigroup energy formulations in slab geometry problems with isotropic scattering and fixed-source. In the present paper, we extend the formulation of the numerical nodal method Spectral Deterministic Method (SDM) (OLIVA et al, 2016;OLIVA et al, 2018), to solve problems in one-dimension slab geometry, in the formulation of discrete ordinates ( ), considering an arbitrary anisotropic scattering of order L in homogeneous and heterogeneous domains with a prescribed interior source.…”

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confidence: 99%

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Método Espectral Determinístico para Problemas de Transporte de Nêutrons na Formulação SN, Multigrupo de Energia, Geometria Unidimensional, Espalhamento Anisotrópico e Fonte Fixa

Oliva¹,

Filho²,

Hernández³

et al. 2020

Cereus

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RESUMO Neste artigo é apresentada uma nova metodologia numérica contemplando o desenvolvimento de um método da classe dos espectro-nodais (malha grossa) para a solução de problemas de transporte de nêutrons na formulação das ordenadas discretas (), em geometria unidimensional, considerando o espalhamento anisotrópico, fonte fixa e multigrupo de energia. O método, denominado Método Espectral Determinístico (MED), baseia-se, inicialmente, na análise espectral das equações de transporte de nêutrons. As incógnitas dessa metodologia são os fluxos angulares nos contornos e o fluxo angular médio no interior dos nodos espaciais. Os valores numéricos obtidos para essas grandezas, a menos dos erros da aritmética finita computacional, concordam com a solução analítica da equação de transporte no domínio espacial utilizado. Os resultados numéricos são mostrados e comparados com o tradicional método de malha fina, DD,cf., Diamond Difference e os métodos nodais SGF, cf., spectral Green's function e o método FN para ilustrar a precisão numérica nos resultados obtidos pelo MED.

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Section: The Multigroup Spectral Deterministic Method(sdm) For Hetementioning

confidence: 99%

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confidence: 99%

Método Espectral Determinístico para Problemas de Transporte de Nêutrons na Formulação SN, Multigrupo de Energia, Geometria Unidimensional, Espalhamento Anisotrópico e Fonte Fixa

Oliva¹,

Filho²,

Hernández³

et al. 2020

Cereus

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“…We can cite as an example the MOC [8,9], cf., Method of Characteristics, the traditional polynomial methods [10][11] and spectral nodal methods, e.g., the SGF method [12][13], cf. spectral Green´s function, the RM method [14], cf., Response Matrix and SDM [15][16][17], cf., Spectral Deterministic Method, that significantly reduce the execution times of the computational codes used in these models, presenting good accuracy in numerical results.…”

Section: Introductionmentioning

confidence: 99%

“…The spectral nodal method SDM [15][16][17] generates the angular fluxes at the interfaces of a onedimensional domain, using Gauss-Legendre quadrature set, in discrete ordinates (S N ) multigroup formulation, in the neutron transport theory. Once the coarse-mesh solution was obtained with the SDM method, we first determined the arbitrary constants of the analytical general solution of the S N equations, treating the term of isotropic scattering source accurately (without approximations) within each spatial node.…”

Section: Introductionmentioning

confidence: 99%

Neutron angular flux reconstruction in slab geometry using multigroup discrete ordinates transport models

Filho

2023

Braz. J. Rad. Sci.

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In this article, we present an application of the coarse-mesh Deterministic Spectral Method (SDM) to generate multigroup angular fluxes in one-dimensional spatial domains using the neutron transport stationary equation, in the formulation of discrete ordinates (SN), considering isotropic scattering source. After obtaining the analytical solution of the SN equations, we replace the integral term of the scattering source in the original neutron transport equation. Thus, we obtain analytically two expressions for angular fluxes in the multigroup formulation, considering the neutron propagation in the positive ( ) and negative ( ) directions, presenting a meaningful reduction in the computational time of simulations of typical neutron shielding problems.

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“…In the work by Oliva et al [9], a novel numerical methodology, framed in the class of the spectralnodal methods for solving multigroup slab-geometry transport equations in non-multiplying media, was presented. This method shows to be algebraically and computationally simpler than other spectral-nodal methods and was termed the Spectral Deterministic Method (SDM).…”

Section: Introductionmentioning

confidence: 99%

The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

et al. 2021

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A new approach for the application of the coarse–mesh Modified Spectral Deterministic method to numerically solve the two–dimensional neutron transport equation in the discrete ordinates (Sn) formulation is presented in this work. The method is based on within node general solution of the conventional one–dimensional Sn transverse integrated equations considering constant approximations for the transverse leakage terms and obtaining the Sn spatial balance equations. The discretized equations are solved by using a modified Source Iteration scheme without additional approximations since the average angular fluxes are computed analytically in each iteration. The numerical algorithm of the method presented here is algebraically simpler than other spectral nodal methods in the literature for the type of problems we have considered. Numerical results to two typical model problems are presented to test the accuracy of the offered method.

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The spectral nodal method applied to multigroup SN neutron transport problems in One-Dimensional geometry with Fixed–Source

Cited by 13 publications

References 3 publications

Método Espectral Determinístico para Problemas de Transporte de Nêutrons na Formulação SN, Multigrupo de Energia, Geometria Unidimensional, Espalhamento Anisotrópico e Fonte Fixa

Método Espectral Determinístico para Problemas de Transporte de Nêutrons na Formulação SN, Multigrupo de Energia, Geometria Unidimensional, Espalhamento Anisotrópico e Fonte Fixa

Neutron angular flux reconstruction in slab geometry using multigroup discrete ordinates transport models

The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

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