Adaptive refinement for P N neutron transport equation based on conjoint variational formulation and discontinuous finite element method

2018 ◽  
Vol 104 ◽  
pp. 16-31 ◽  
Author(s):  
KH. Sadeghi ◽  
M. Abbasi ◽  
A. Zolfaghari
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transport Equation ◽  
Variational Formulation ◽  
Neutron Transport ◽  
Adaptive Refinement ◽  
Neutron Transport Equation ◽  
Discontinuous Finite Element ◽  
Discontinuous Finite Element Method ◽  
Element Method

scholarly journals A Comparative Analysis of Neutron Transport Calculations Based on Variational Formulation and Finite Element Approaches

Energies ◽  
2020 ◽  
Vol 13 (20) ◽  
pp. 5424
Author(s):  
Khashayar Sadeghi ◽  
Seyed Hadi Ghazaie ◽  
Ekaterina Sokolova ◽  
Ahmad Zolfaghari ◽  
Mohammad Reza Abbasi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Formulation ◽  
Numerical Solutions ◽  
Neutron Transport ◽  
Computational Error ◽  
Fine Mesh ◽  
Discontinuous Finite Element ◽  
Discontinuous Finite Element Method ◽  
Element Method

The application of continuous and discontinuous approaches of the finite element method (FEM) to the neutron transport equation (NTE) has been investigated. A comparative algorithm for analyzing the capability of various types of numerical solutions to the NTE based on variational formulation and discontinuous finite element method (DFEM) has been developed. The developed module is coupled to the program discontinuous finite element method for neutron (DISFENT). Each variational principle (VP) is applied to an example with drastic changes in the distribution of neutron flux density, and the obtained results of the continuous and discontinuous finite element (DFE) have been compared. The comparison between the level of accuracy of each approach using new module of DISFENT program has been performed based on the fine mesh solutions of the multi-PN (MPN) approximation. The obtained results of conjoint principles (CPs) have been demonstrated to be very accurate in comparison to other VPs. The reduction in the number of required meshes for solving the problem is considered as the main advantage of this principle. Finally, the spatial additivity to the context of the spherical harmonics has been implemented to the CP, to avoid from computational error accumulation.

Determinant Methods for Solving Neutron Transport Equation in Unstructured Geometry

2010 ◽  
Author(s):  
Hongchun Wu ◽  
Guoming Liu ◽  
Liangzhi Cao ◽  
Qichang Chen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fuel Assembly ◽  
Transport Equation ◽  
Neutron Transport ◽  
Transmission Probability ◽  
Probability Method ◽  
Neutron Transport Equation ◽  
Nodal Method ◽  
Element Method

The spherical harmonics (Pn) finite element method, the Sn finite element method, the triangle transmission probability method and the discrete triangle nodal method were all introduced to solve the neutron transport equation for unstructured fuel assembly respectively. The computing codes of each method were encoded and numerical results were discussed and compared. It was demonstrated that these four methods can solve neutron transport equations with unstructured-meshes very effectively and correctly, they can be used to solve unstructured fuel assembly problem.

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