An improved variational nodal method for the solution of the three-dimensional steady-state multi-group neutron transport equation

2018 ◽  
Vol 337 ◽  
pp. 419-427 ◽  
Author(s):  
Tengfei Zhang ◽  
Hongchun Wu ◽  
Liangzhi Cao ◽  
Yunzhao Li
Keyword(s):  
Steady State ◽  
Transport Equation ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Neutron Transport Equation ◽  
Nodal Method

scholarly journals Note on the Solution of Transport Equation by Tau Method and Walsh Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Abdelouahab Kadem ◽  
Adem Kilicman
Keyword(s):  
Transport Equation ◽  
Legendre Polynomials ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Walsh Function ◽  
Dimensional Case ◽  
Angular Variable ◽  
Tau Method ◽  
Algebraic Equations ◽  
Neutron Transport Equation

We consider the combined Walsh function for the three-dimensional case. A method for the solution of the neutron transport equation in three-dimensional case by using the Walsh function, Chebyshev polynomials, and the Legendre polynomials are considered. We also present Tau method, and it was proved that it is a good approximate to exact solutions. This method is based on expansion of the angular flux in a truncated series of Walsh function in the angular variable. The main characteristic of this technique is that it reduces the problems to those of solving a system of algebraic equations; thus, it is greatly simplifying the problem.

scholarly journals A SPLITTING ITERATIVE METHOD FOR SOLVING THE NEUTRON TRANSPORT EQUATION

2009 ◽  
Vol 14 (3) ◽  
pp. 271-289 ◽  
Author(s):  
Onana Awono ◽  
Jacques Tagoudjeu
Keyword(s):  
Steady State ◽  
Iterative Method ◽  
Transport Equation ◽  
Multigrid Method ◽  
Neutron Transport ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Neutron Transport Equation ◽  
Slab Geometry

This paper presents an iterative method based on a self‐adjoint and m‐accretive splitting for the numerical treatment of the steady state neutron transport equation. Theoretical analysis shows that this method converges unconditionally to the unique solution of the transport equation. The convergence of the method is numerically illustrated and compared with the standard Source Iteration method and multigrid method on sample problems in slab geometry and in two dimensional space.

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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