Discrete ordinates method for three-dimensional neutron transport equation based on unstructured-meshes

2008 ◽  
Vol 2 (2) ◽  
pp. 179-182
Author(s):  
Haitao Ju ◽  
Hongchun Wu ◽  
Dong Yao ◽  
Chunyu Xian
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Unstructured Meshes ◽  
Discrete Ordinates ◽  
Neutron Transport Equation ◽  
Discrete Ordinates Method

THE DISCRETE ORDINATES METHOD FOR THE NEUTRON TRANSPORT EQUATION IN AN INFINITE CYLINDRICAL DOMAIN

1992 ◽  
Vol 02 (03) ◽  
pp. 317-338 ◽  
Author(s):  
MOHAMMAD ASADZADEH ◽  
PETER KUMLIN ◽  
STIG LARSSON
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Regularity Result ◽  
Discrete Ordinates ◽  
Cylindrical Domain ◽  
Neutron Transport Equation ◽  
Scalar Flux ◽  
Weakly Singular Kernel ◽  
Discrete Ordinates Method ◽  
Weakly Singular

We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain. The theorem states that the solution has almost two derivatives in L1, and is proved using Besov space techniques. This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation. We derive an error estimate in the L1-norm for the scalar flux, and as a consequence, we obtain an error bound for the critical eigenvalue.

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.

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