A boundary value problem for the three dimensional neutron transport equation

1979 ◽  
Vol 71 (1) ◽  
pp. 63-98
Author(s):  
Joseph G. Conlon
Keyword(s):  
Boundary Value Problem ◽  
Transport Equation ◽  
Neutron Transport ◽  
Boundary Value ◽  
Three Dimensional ◽  
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.

Transmission Probability Method Based on Triangular-Z Mesh for Solving Neutron Transport Equation in Three-Dimensional Geometry

2008 ◽  
Author(s):  
Guoming Liu ◽  
Hongchun Wu
Keyword(s):  
Transport Equation ◽  
Present Method ◽  
Flux Distribution ◽  
Monte Carlo Calculation ◽  
Neutron Transport ◽  
Three Dimensional ◽  
Transmission Probability ◽  
Benchmark Problems ◽  
Probability Method ◽  
Neutron Transport Equation

This paper presents a transmission probability method (TPM) to solve the neutron transport equation in three-dimensional triangular-z geometry. The neutron source within the mesh is assumed to be spatially uniform and isotropic. On the mesh surface, the constant and the simplified P1 approximation are invoked for the anisotropic angular neutron flux distribution. Based on this model, a code TPMTDT is encoded. It was verified by three 3D Takeda benchmark problems, in which the first two problems are in XYZ geometry and the last one is in hexagonal-z geometry. The numerical results of the present method agree well with those of Monte-Carlo calculation method and Spherical Harmonics (PN) method.

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