On the Neutron multi-group kinetic diffusion equation in a heterogeneous slab: An exact solution on a finite set of discrete points

Ceolin, Celina; Schramm, Marcelo; Vilhena, Marco T.; Bodmann, B. E. J.

doi:10.1016/j.anucene.2014.09.038

Cited by 16 publications

(2 citation statements)

References 9 publications

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“…One of the first methods used for solving this eigenvalue problem was the finite difference method (FDM), however as it requires very mesh points to model accurately, it becomes a bit slow from the computational point of view [1]. Over time other methodologies have been implemented for solving the neutron diffusion eigenvalue problem, as for example: Finite Element Method [2], [Pseudo-Harmonics Expansion Method [1], Finite Volume Method [3], Lagrange Polynomial Algorithms (LAP) using the same approach in FDM [4], Taylor Series Expansion Method [5], Isogeometric Analysis [6], Integral Transform Techniques [7] and Generalized Integral Transform Technique (GITT) combined with Laplace Transform given by [8] and Nodal Method [9].…”

Section: Introductionmentioning

confidence: 99%

Solution of the Multigroup Neutron Diffusion Eigenvalue Problem in Slab Geometry by Modified Power Method

Zanette¹,

Petersen²,

Tavares³

2021

Braz. J. Rad. Sci.

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We describe in this work the application of the modified power method for solve the multigroup neutron diffusion eigenvalue problem in slab geometry considering two-dimensions for nuclear reactor global calculations. It is well known that criticality calculations can often be best approached by solving eigenvalue problems. The criticality in nuclear reactors physics plays a relevant role since establishes the ratio between the numbers of neutrons generated in successive fission reactions. In order to solve the eigenvalue problem, a modified power method is used to obtain the dominant eigenvalue (effective multiplication factor) and its corresponding eigenfunction (scalar neutron flux), which is non-negative in every domain, that is, physically relevant. The innovation of this work is solving the neutron diffusion equation in analytical form for each new iteration of the power method. For solve this problem we propose to apply the Finite Fourier Sine Transform on one of the variables obtaining a transformed problem which is resolved by well-established methods for ordinary differential equations. The inverse Fourier Transform is used to reconstruct the solution for the original problem. It is known that the power method is an iterative source method in which is updated by the neutron flux expression of previous iteration. Thus, for each new iteration, the neutron flux expression becomes larger and more complex due to analytical solution what makes us propose that it be reconstructed through a polynomial interpolation. The methodology is implemented to solve a homogeneous problem and the results are compared with works presents in the literature.

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Section: Introductionmentioning

confidence: 99%

Solution of the Multigroup Neutron Diffusion Eigenvalue Problem in Slab Geometry by Modified Power Method

Zanette¹,

Petersen²,

Tavares³

2021

Braz. J. Rad. Sci.

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“…As ECE na teoria da difusão de nêutrons são amplamente utilizadas por fornecer resultados satisfatórios para cálculos globais em física de reatores [6]. Ao longo dos anos, diversas metodologia foram propostas para solucionar este problema da cinética espacial, por exemplo, por diferenças finitas [12], por expansão em séries [4], pelo método ortogonal quase estático [9], entre outras. Além da relevância do ponto de vista físico, os sistemas são rígidos e o tratamento numérico é desafiador.…”

Section: Introductionunclassified

Cinética espacial na teoria da difusão de nêutrons: uma solução via abordagens noclais e exponenciais matriciais

Zanette

Barichello

Petersen

2021

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. Neste trabalho, uma solução para o problema da cinética espacial na teoria da difusão de nêutrons multigrupo em geometria cartesiana unidimensional é derivada. A partir da divisão do domínio espacial em nodos homogêneos, uma integração nodal é aplicada nas equações da cinética espacial, obtendo variáveis médias em cada nodo: fluxos, concentrações de precursores e densidades de correntes. As densidades de correntes para cada interface são aproximadas pela média ponderada dos coeficientes de difusão e pelos fluxos médios. Uma solução analítica na variável temporal na forma de uma exponencial matricial é proposta e, essa exponencial matricial, é avaliada pela aproximação de Padé e pelo método de Schur-Parlett. Os resultados numéricos obtidos são comparáveis aos resultados existentes na literatura e o método de Schur-Parlett mostra uma maior eficiência à aproximação de Padé.

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On the Mono-Energetic Neutron Space Kinetics Equation in Cartesian Geometry: An Analytic Solution by a Spectral Method

Tumelero

Vilhena

Bodmann

2022

Integral Methods in Science and Engineering

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On the Neutron multi-group kinetic diffusion equation in a heterogeneous slab: An exact solution on a finite set of discrete points

Cited by 16 publications

References 9 publications

Solution of the Multigroup Neutron Diffusion Eigenvalue Problem in Slab Geometry by Modified Power Method

Solution of the Multigroup Neutron Diffusion Eigenvalue Problem in Slab Geometry by Modified Power Method

Cinética espacial na teoria da difusão de nêutrons: uma solução via abordagens noclais e exponenciais matriciais

On the Mono-Energetic Neutron Space Kinetics Equation in Cartesian Geometry: An Analytic Solution by a Spectral Method

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