scholarly journals The influence of half-range quadrature scheme on ADO method convergence

2019 ◽  
Vol 15 (4) ◽  
Author(s):  
Dalvana Lopes Ribeiro ◽  
João Francisco Prolo Filho
Keyword(s):  
Neutron Transport ◽  
Computational Cost ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Scalar Fluxes ◽  
Quadrature Scheme ◽  
Anisotropic Problems ◽  
Ado Method ◽  
Software Distribution ◽  
State Regime

In this work, a discrete ordinates solution for a neutron transport problem in one-dimensional Cartesian geometry is presented. In order to evaluate the efficiency of the half-range quadrature scheme, the Analytical Discrete Ordinates method (ADO) is used to solve two classes of problems in finite and homogeneous media (with isotropic and linear anisotropic scattering), for steady-state regime, without inner source and prescribed boundary conditions. Numerical results for the scalar fluxes were obtained and comparisons with other works in the literature were made. The versatility of the use of quadratures has always been seen as an advantage of the ADO method which, besides providing accurate results at a low computational cost, has a simpler approach, allowing the use of free software distribution for the simulations. In the results analysis, it was verified that the use of the half-range quadrature was able to accelerate the convergence, mainly in linearly anisotropic problems.

scholarly journals On the spectrum of discrete-ordinates neutron transport problems

2021 ◽  
Vol 9 (2) ◽  
Author(s):  
Jesús Pérez Curbelo
Keyword(s):  
Discrete Spectrum ◽  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
High Anisotropy ◽  
Linear Transport Equation ◽  
The One ◽  
Transport Problems ◽  
Theoretical Results ◽  
Analytic Problem

Over the last six decades, the discrete spectrum of the neutron transport operator has been widely studied. Important theoretical results can be found in the literature regarding the one-speed linear transport equation with anisotropic scattering. In this work, the discrete-ordinates (SN) transport problem with anisotropic scattering has been considered and the discrete spectrum results in multiplying media have been corroborated. The numerical results obtained for the dominant SN eigenvalues agreed with the ones for the analytic problem reported in the literature up to a triplet scattering order. A compact methodology to perform the spectral analysis to multigroup SN problems with high anisotropy order in the scattering and fission reactions is also presented in this paper.

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.

scholarly journals Spectral Nodal Methodology for Multigroup Slab-Geometry Discrete Ordinates Neutron Transport Problems with Linearly Anisotropic Scattering

2021 ◽  
Vol 8 (3B) ◽  
Author(s):  
Amaury Muñoz Oliva ◽  
Hermes Alves Filho ◽  
Davi José Martins e Silva ◽  
Carlos Rafael García Hernández
Keyword(s):  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Slab Geometry ◽  
Transport Problems

scholarly journals THE ADO METHOD FOR SOLVING ONE-DIMENSIONAL DEEP-PENETRATION TRANSPORT PROBLEMS

2019 ◽  
Vol 18 (1) ◽  
pp. 92
Author(s):  
D. L. Ribeiro ◽  
M. P. Rodrigues ◽  
J. F. Prolo Filho
Keyword(s):  
Computational Cost ◽  
Anisotropic Scattering ◽  
Deep Penetration ◽  
Test Problems ◽  
One Dimensional ◽  
Scattering Effects ◽  
Ado Method ◽  
Cartesian Geometry ◽  
The Media ◽  
Transport Problems

In this work, the Analytical Discrete Ordinate method (ADO method) is used to solve deep-penetration transport problems in one-dimensional Cartesian geometry, subject to isotropic and linear anisotropic scattering effects. The regime is considered permanent, the media are homogeneous, and the fluxes are caused by sources located on the boundaries of the domain. In addition, the energy fluctuations will be considered as not significant, characterizing the phenomena as monoenergetic problems. In order to validate the code, method and provide benchmark results, some test problems will be treated and results will be discussed. In particular, the ADO method generated fairly accurate results when compared to other methods based on SN approaches, at a relatively low computational cost.

scholarly journals Formulação nodal aplicada à problemas de transporte bidimensional em geometria cartesiana

2015 ◽  
Vol 11 (8) ◽  
Author(s):  
Carlos Eduardo Souza Ferreira ◽  
Leonardo Ramos Emmendorfer ◽  
João Francisco Prolo Filho
Keyword(s):  
Neutron Transport ◽  
Computational Cost ◽  
Coupled System ◽  
Two Dimensional ◽  
Discrete Ordinate ◽  
One Dimensional ◽  
Scalar Fluxes ◽  
Cartesian Geometry ◽  
Transport Problems ◽  
Low Computational Cost

<div><p class="SPabstract">Neste trabalho, uma formulação nodal é proposta para o tratamento de uma classe de problemas de transporte de nêutrons, em geometria cartesiana bidimensional. Através do processo de integração, equações unidimensionais são obtidas, reescrevendo o modelo em termos de quantidades médias. A resolução das equações integradas é feita através de uma versão do método de Ordenadas Discretas Analítico (ADO), onde também são obtidas soluções explicitas, analíticas em termos das variáveis espaciais, através de um código de fácil implementação. Pode-se destacar também como vantagens desta formulação a versatilidade na escolha da quadratura e o baixo custo computacional, uma vez que esquemas iterativos não são necessários tampouco a subdivisão do domínio em células. Para lidar como os termos do contorno que surgem no processo, propõe-se aqui uma representação por constantes, de forma que as equações nas variáveis x e y são tratadas através de um sistema acoplado. Resultados obtidos por esta formulação são apresentados, bem como alguns perfis de fluxos escalares. </p></div><p><strong>Nodal formulation applied to two-dimensional transport problems in Cartesian geometry.</strong></p><p> In this paper, a nodal formulation is proposed for the treatment of a class of neutron transport problems in two-dimensional Cartesian geometry. By the integration process, one-dimensional equations are obtained, rewriting the model in terms of average quantities. The resolution of the integrated equations is made using a version of the Analytical Discrete Ordinate method (ADO), where also be obtained explicit solutions, analytical in terms of spatial variables, through an easy implementation code. It can also highlight as advantages of this formulation the versatility of the quadrature choice and the low computational cost, since iterative schemes are not needed either subdividing the domain in cells. To deal with the contour terms that arise in the process, is proposed here a representation by constants, so that the equations in the variables x and y are treated through a coupled system. Results obtained by this formulation are presented, as well as some profiles of scalar fluxes. </p>

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