scholarly journals Discrete Ordinates Numerical Integration Method for Neutron Transport Equation in Slab Geometry

1968 ◽  
Vol 5 (7) ◽  
pp. 342-349 ◽  
Author(s):  
Kiyoshi TAKEUCHI ◽  
Iwao KATAOKA
Keyword(s):  
Transport Equation ◽  
Numerical Integration ◽  
Integration Method ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Numerical Integration Method ◽  
Neutron Transport Equation ◽  
Slab Geometry

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.

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.

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