Two-dimensional Haar wavelet Collocation Method for the solution of Stationary Neutron Transport Equation in a homogeneous isotropic medium

2014 ◽  
Vol 70 ◽  
pp. 30-35 ◽  
Author(s):  
A. Patra ◽  
S. Saha Ray
Keyword(s):  
Transport Equation ◽  
Collocation Method ◽  
Isotropic Medium ◽  
Neutron Transport ◽  
Haar Wavelet ◽  
Two Dimensional ◽  
Neutron Transport Equation ◽  
Wavelet Collocation Method

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.

Solution and Study of the Two-Dimensional Nodal Neutron Transport Equation

2002 ◽  
Author(s):  
Ruben Panta Pazos ◽  
Marco Tullio de Vilhena ◽  
Eliete Biasotto Hauser
Keyword(s):  
Transport Equation ◽  
Truncation Error ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Angular Variable ◽  
Two Dimensional ◽  
Neutron Transport Equation ◽  
Discrete Approximations ◽  
Integral Term ◽  
The Laplace Transform

In the last decade Vilhena and coworkers10 reported an analytical solution to the two-dimensional nodal discrete-ordinates approximations of the neutron transport equation in a convex domain. The key feature of these works was the application of the combined collocation method of the angular variable and nodal approach in the spatial variables. By nodal approach we mean the transverse integration of the SN equations. This procedure leads to a set of one-dimensional SN equations for the average angular fluxes in the variables x and y. These equations were solved by the old version of the LTSN method9, which consists in the application of the Laplace transform to the set of nodal SN equations and solution of the resulting linear system by symbolic computation. It is important to recall that this procedure allow us to increase N the order of SN up to 16. To overcome this drawback we step forward performing a spectral painstaking analysis of the nodal SN equations for N up to 16 and we begin the convergence of the SN nodal equations defining an error for the angular flux and estimating the error in terms of the truncation error of the quadrature approximations of the integral term. Furthermore, we compare numerical results of this approach with those of other techniques used to solve the two-dimensional discrete approximations of the neutron transport equation6.

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