Coarse-Mesh Angular Dependent Rebalance Acceleration of the Discrete Ordinates Transport Calculations

2004 ◽  
Vol 148 (3) ◽  
pp. 355-373 ◽  
Author(s):  
Young Ryong Park ◽  
Nam Zin Cho
Keyword(s):  
Discrete Ordinates ◽  
Coarse Mesh

scholarly journals The modified spectral deterministic method applied to fixed–source discrete ordinates problems in X,Y–geometry

2021 ◽  
Vol 8 (3A) ◽  
Author(s):  
Jesús Pérez Curbelo ◽  
Rafael Barbosa Libotte ◽  
Amaury Muñoz Oliva ◽  
Ricardo Carvalho Barros ◽  
Hermes Alves Filho
Keyword(s):  
Neutron Transport ◽  
Iteration Scheme ◽  
Discrete Ordinates ◽  
Coarse Mesh ◽  
Neutron Transport Equation ◽  
Balance Equations ◽  
Deterministic Method ◽  
New Approach ◽  
One Dimensional ◽  
Typical Model

A new approach for the application of the coarse–mesh Modified Spectral Deterministic method to numerically solve the two–dimensional neutron transport equation in the discrete ordinates (Sn) formulation is presented in this work. The method is based on within node general solution of the conventional one–dimensional Sn transverse integrated equations considering constant approximations for the transverse leakage terms and obtaining the Sn spatial balance equations. The discretized equations are solved by using a modified Source Iteration scheme without additional approximations since the average angular fluxes are computed analytically in each iteration. The numerical algorithm of the method presented here is algebraically simpler than other spectral nodal methods in the literature for the type of problems we have considered. Numerical results to two typical model problems are presented to test the accuracy of the offered method.

scholarly journals A NOVEL COARSE-MESH METHOD APPLIED TO NEUTRON SHIELDING PROBLEMS USING THE MULTIGROUP TRANSPORT THEORY IN DISCRETE ORDINATES FORMULATIONS

2021 ◽  
Vol 8 (3A) ◽  
Author(s):  
Rafael Barbosa Libotte ◽  
Hermes Alves Filho ◽  
Ricardo Carvalho De Barros
Keyword(s):  
Transport Theory ◽  
Computational Cost ◽  
Discrete Ordinates ◽  
Coarse Mesh ◽  
Deterministic Method ◽  
Neutron Shielding ◽  
Scalar Fluxes ◽  
Fine Mesh ◽  
Linearized Boltzmann Equation ◽  
Mesh Method

In this paper, we propose a new deterministic numerical methodology to solve the one-dimensional linearized Boltzmann equation applied to neutron shielding problems (fixed-source), using the transport equation in the discrete ordinates formulation (SN) considering the multigroup theory. This is a hybrid methodology, entitled Modified Spectral Deterministic Method (SDM-M), that derives from the Spectral Deterministic Method (SDM) and Diamond Difference (DD) methods. This modification in the SDM method aims to calculate neutron scalar fluxes with lower computational cost. Two model-problems are solved using the SDM-M, and the results are compared to the coarse-mesh methods SDM, Spectral Green's Function (SGF) and Response Matrix (RM), and the fine-mesh method DD. The numerical results were obtained in the programming language JAVA version 1.8.0_91.

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