Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry

Barros, Ricardo C.; Filho, Hermes Alves; Platt, Gustavo Mendes; Oliveira, Francisco Bruno Souza; Militão, Damiano S.

doi:10.1016/j.anucene.2010.06.019

Cited by 6 publications

(6 citation statements)

References 7 publications

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“…It is important to observe that, in this formulation, from a set of discrete ordinates equations, an eigenvalue problem of order / was derived, which means a relevant gain in comparison with other similar discrete ordinates approaches, where characteristic equations or eigensystems of order are obtained, for the same quadrature scheme [16]. Furthermore, the expressions for the homogeneous solutions, in terms of spatial variable, are analytical, contributing to the low computational cost and high accuracy of the method.…”

Section: The Ado Methodsmentioning

confidence: 99%

“…In order to calculate the disadvantage factor, Barros et al (2010) [16] and Maiorino and Siewert (1980) [9] works were used as a basis, and the discrete ordinates version for a neutron transport equation in one-dimensional Cartesian geometry, applied to a layered heterogeneous medium with linearly anisotropic scattering, in steady-state regime, is written as…”

Section: Mathematical Modelmentioning

confidence: 99%

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Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects

Filho

Rodrigues

2017

Sci. Plena

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Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects Aplicação do método ADO no cálculo do fator de desvantagem para células heterogêneas planas considerando efeitos de espalhamento anisotrópico linear Neste trabalho, o cálculo do fator de desvantagem é feito por uma versão do método de Ordenadas do Discretas Analítico (método ADO). Para isso, será considerada uma classe de problemas de transporte de nêutrons unidimensionais em geometria Cartesiana, com efeitos de espalhamento linearmente anisotrópicos em meios heterogêneos em camadas. O processo consiste em aplicar a discretização angular SN, convertendo a equação de transporte integro-diferencial em um sistema de equações diferenciais ordinárias, cuja solução homogênea é obtida por um problema de autovalores quadráticos com ordem reduzida. Para estabelecer uma solução de forma fechada para esta classe de problemas, soluções particulares em termos de constantes são usadas, bem como condições de fronteira reflexivas e condições de interface. Afim de validar o código, o método e para fornecer resultados benchmark, uma classe problemas em duas camadas é tratado. Uma breve discussão sobre a influência da anisotropia é feita e aspectos numéricos são discutidos.Palavras-chave: meio heterogêneo, espalhamento anisotropico, equação de transporte unidimensionalIn this work, the disadvantage-factor calculation is performed by a version of the Analytical Discrete Ordinates method (ADO method). For this, a class of one-dimenisional neutron transport problems in Cartesian geometry, with linearly anisotropic scattering effects in layered heterogeneous media, will be considered. The process consists in applying the angular discretization SN, converting the integrodifferential transport equation into an ordinary differential equations system, which homogeneous solution is obtained by a quadratic eigenvalues problem with reduced order. To establish a closed form solution for this class of problems, particular solutions in terms of constants are used, as well as reflective boundary conditions and interface conditions. In order to validate the code, the method and to provide benchmark results, a class of two-layered problems is treated. A brief discussion on the influence of anisotropy is made and numerical aspects are discussed.

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Section: The Ado Methodsmentioning

confidence: 99%

Section: Mathematical Modelmentioning

confidence: 99%

Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects

Filho

Rodrigues

2017

Sci. Plena

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“…In these cases, the mathematical model used is the neutron transport equation. The deterministic methods' use to solve neutron transport problems is widely reported in the scientific literature (Alcouffe et al, 1979;Larsen, 1986; Barros and Larsen, 1990; Barros et al, 1998;Filho et al, 2002;Dominguez and Barros, 2007;Barros et al, 2010;Menezes et al, 2014;Silva et al, 2015). In many instances, it is common to use the multi-group discrete ordinate formulation (S N ) of neutron transport equation as the mathematical model (Lewis and Miller, 1984).…”

Section: Introductionmentioning

confidence: 99%

“…The first spectral nodal method, described in Barros and Larsen (1990) called spectral Green's function method (SGF) was developed to solve problems with fixed-source, one-dimensional Cartesian geometry, and one-energy group. From this point, various authors extended the SGF methods for several groups, anisotropic source term, different geometries and transport equation formulations, both for fixed-source like (Barros and Larsen, 1991; Barros and Larsen, 1992;Anli and Gungor, 1996;Barros, 1997; Barros et al, 1998;Mello and Barros, 2002;Dominguez and Barros, 2007;Barros et al, 2010;Menezes et al, 2014) as well as for eigenvalue problems (Abreu et al, 1996;Barros et al, 1999;Filho et al, 2002;Barros et al, 2003;Silva et al, 2015). The main advantages of SGF methods are their high accuracy and weak spatial dependence.…”

Section: Introductionmentioning

confidence: 99%

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

Ortiz

Domínguez

Hernández

et al. 2019

IJNEST

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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 quasianalytical 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 71 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.

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“…The deterministic methods' use to solve neutron transport problems is widely reported in the scientific literature (Alcouffe et al, 1979;Larsen, 1986;Barros and Larsen, 1990;Barros et al, 1998;Filho et al, 2002;Dominguez and Barros, 2007;Barros et al, 2010;Menezes et al, 2014;Silva et al, 2015). In many instances, it is common to use the multi-group discrete ordinate formulation (S N ) of neutron transport equation as the mathematical model (Lewis and Miller, 1984).…”

Section: Introductionmentioning

confidence: 99%

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

Rivas-Ortiz

Domínguez

Hernández

et al. 2019

IJNEST

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Analytical reconstruction scheme for the coarse-mesh solution generated by the spectral nodal method for neutral particle discrete ordinates transport model in slab geometry

Cited by 6 publications

References 7 publications

Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects

Application of the ADO method on disadvantage-factor calculation for heterogeneous slab cells considering linear anisotropic scattering effects

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

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

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