Shifting Strategy in the Spectral Analysis for the Spectral Green’s Function Nodal Method for Slab-Geometry Adjoint Transport Problems in the Discrete Ordinates Formulation

2017 ◽  
pp. 201-210
Author(s):  
J. P. Curbelo ◽  
O. P. da Silva ◽  
C. R. García ◽  
R. C. Barros
Keyword(s):  
Spectral Analysis ◽  
Green’S Function ◽  
Green's Function ◽  
Discrete Ordinates ◽  
Slab Geometry ◽  
Nodal Method ◽  
Shifting Strategy ◽  
Adjoint Transport ◽  
Transport Problems

scholarly journals An Extended Linear Discontinuous Method for One-group Fixed Source Discrete Ordinates Problems with Isotropic Scattering in Slab Geometry

2019 ◽  
Vol 20 (1) ◽  
pp. 61
Author(s):  
Iram Barbaro Rivas-Ortiz ◽  
Dany Sanchez Dominguez ◽  
Carlos Rafael Garcia Hernandez ◽  
Susana Marrero Iglesias ◽  
Alberto Escrivá
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Isotropic Scattering ◽  
Benchmark Problems ◽  
Discrete Ordinates ◽  
Auxiliary Equation ◽  
Slab Geometry ◽  
Spectral Parameters ◽  
Computational Performance ◽  
Discontinuous Approximation

Nowadays, the obtainment of an accurate numerical solution of fixed source discrete ordinates problems is relevant in many areas of engineering and science. In this work, we extend the hybrid Finite Element Spectral Green's Function method (FEM-SGF), originally developed to solve eigenvalue diffusion problems, for fixed source problems using as a mathematical model, the discrete ordinates formulation in one energy group with isotropic scattering in slab geometry. This new method, Extended Linear Discontinuous Discrete Ordinates (ELD-SN), is based on the use of neutron balance equations and the construction of a hybrid auxiliary equation. This auxiliary equation combines a linear discontinuous approximation and spectral parameters to approximate the neutron angular flux inside the cell. Numerical results for benchmark problems are presented to illustrate the accuracy and computational performance of our methodology. ELD-SN method is free from spatial truncation errors in S2 quadrature, and generate good results in the other quadrature sets. This method is more accurate than the conventional Diamond Difference (DD) and Linear Discontinuous (LD) methods, but surpassed by the Spectral Green's Function (SGF) method, for quadrature order greater than two.

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