Solution of neutron diffusion equation in 2d polar (r,θ) coordinates using Nodal Integral Method

2017 ◽  
Vol 105 ◽  
pp. 69-78 ◽  
Author(s):  
Manish Raj ◽  
Suneet Singh
Keyword(s):  
Diffusion Equation ◽  
Integral Method ◽  
Neutron Diffusion ◽  
Nodal Integral Method ◽  
Neutron Diffusion Equation

Variational nodal method for three-dimensional multigroup neutron diffusion equation based on arbitrary triangular prism

2021 ◽  
Vol 158 ◽  
pp. 108285
Author(s):  
Kun Zhuang ◽  
Wen Shang ◽  
Ting Li ◽  
Jiangtao Yan ◽  
Sipeng Wang ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Three Dimensional ◽  
Triangular Prism ◽  
Neutron Diffusion ◽  
Nodal Method ◽  
Multigroup Neutron ◽  
Neutron Diffusion Equation

scholarly journals Block hybrid multilevel method to compute the dominant λ-modes of the neutron diffusion equation

2018 ◽  
Vol 121 ◽  
pp. 513-524 ◽  
Author(s):  
A. Carreño ◽  
A. Vidal-Ferràndiz ◽  
D. Ginestar ◽  
G. Verdú
Keyword(s):  
Diffusion Equation ◽  
Neutron Diffusion ◽  
Multilevel Method ◽  
Neutron Diffusion Equation

Improved nodal expansion method for solving neutron diffusion equation in cylindrical geometry

2010 ◽  
Vol 240 (8) ◽  
pp. 1997-2004 ◽  
Author(s):  
Dengying Wang ◽  
Fu Li ◽  
Jiong Guo ◽  
Jinfeng Wei ◽  
Jingyu Zhang ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Expansion Method ◽  
Cylindrical Geometry ◽  
Neutron Diffusion ◽  
Nodal Expansion Method ◽  
Neutron Diffusion Equation

Application of linear-extended neutron diffusion equation in a semi-infinite homogeneous medium

2011 ◽  
Vol 38 (2-3) ◽  
pp. 713-719 ◽  
Author(s):  
Gilberto Espinosa-Paredes ◽  
Rodolfo Vázquez-Rodríguez
Keyword(s):  
Diffusion Equation ◽  
Homogeneous Medium ◽  
Neutron Diffusion ◽  
Neutron Diffusion Equation

Refined Algorithm for Solving High-Order Harmonics of Multi Group Neutron Diffusion Equation

2017 ◽  
Author(s):  
Gaoxin Zhou ◽  
Zhi Gang
Keyword(s):  
Diffusion Equation ◽  
Iteration Method ◽  
Krylov Subspace ◽  
Krylov Subspace Method ◽  
Neutron Diffusion ◽  
Subspace Method ◽  
Arnoldi Method ◽  
Arnoldi Algorithm ◽  
Eigenvalue And Eigenvector ◽  
Neutron Diffusion Equation

In recent years, high order harmonic (or eigenvector) of neutron diffusion equation has been widely used in on-line monitoring system of reactor power. There are two kinds of calculation method to solve the equation: corrected power iteration method and Krylov subspace methods. Fu Li used the corrected power iteration method. When solving for the ith harmonic, it tries to eliminate the influence of the front harmonics using the orthogonality of the harmonic function. But its convergence speed depends on the occupation ratio. When the dominant ratios equal to 1 or close to 1, convergence speed of fixed source iteration method is slow or convergence can’t be achieved. Another method is the Krylov subspace method, the main idea of this method is to project the eigenvalue and eigenvector of large-scale matrix to a small one. Then we can solve the small matrix eigenvalue and eigenvector to get the large ones. In recent years, the restart Arnoldi method emerged as a development of Krylov subspace method. The method uses continuous reboot Arnoldi decomposition, limiting expanding subspace, and the orthogonality of the subspace is guaranteed using orthogonalization method. This paper studied the refined algorithms, a method based on the Krylov subspace method of solving eigenvalue problem for large sparse matrix of neutron diffusion equation. Two improvements have been made for a restarted Arnoldi method. One is that using an ingenious linear combination of the refined Ritz vector forms an initial vector and then generates a new Krylov subspace. Another is that retaining the refined Ritz vector in the new subspace, called, augmented Krylov subspace. This way retains useful information and makes the resulting algorithm converge faster. Several numerical examples are the new algorithm with the implicitly restart Arnoldi algorithm (IRA) and the implicitly restarted refined Arnoldi algorithm (IRRA). Numerical results confirm efficiency of the new algorithm.

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