scholarly journals DISCRETE ORDINATES ANGULAR QUADRATURE OF THE NEUTRON TRANSPORT EQUATION

1964 ◽  
Author(s):  
K. D. Lathrop ◽  
B. G. Carlson
Keyword(s):  
Transport Equation ◽  
Neutron Transport ◽  
Discrete Ordinates ◽  
Neutron Transport Equation

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.

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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