scholarly journals Diffusive limit with geometric correction of unsteady neutron transport equation

2017 ◽  
Vol 10 (4) ◽  
pp. 1163-1203 ◽  
Author(s):  
Lei Wu ◽  
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Geometric Correction ◽  
Neutron Transport Equation ◽  
Diffusive Limit

scholarly journals Regularity of Milne problem with geometric correction in 3D

2017 ◽  
Vol 27 (03) ◽  
pp. 453-524 ◽  
Author(s):  
Yan Guo ◽  
Lei Wu
Keyword(s):  
Boundary Conditions ◽  
Transport Equation ◽  
Convex Domain ◽  
Neutron Transport ◽  
Geometric Correction ◽  
Neutron Transport Equation ◽  
Milne Problem ◽  
Diffusive Boundary

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish [Formula: see text]-regularity for its solutions. Combined with a uniform [Formula: see text]-estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.

High-Dimensional Model Representations for the Neutron Transport Equation

2014 ◽  
Vol 177 (3) ◽  
pp. 350-360 ◽  
Author(s):  
Zhengzheng Hu ◽  
Ralph C. Smith ◽  
Jeffrey Willert ◽  
C. T. Kelley
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
High Dimensional ◽  
Dimensional Model ◽  
Neutron Transport Equation

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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