On the application of the ADO method to the solution of two-dimensional radiative transfer problems in anisotropic scattering media

Barichello, Liliane Basso; Rui, Karine; Cunha, Rudnei Dias da

doi:10.1016/j.ijthermalsci.2022.107685

Cited by 6 publications

(4 citation statements)

References 35 publications

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“…In another application of the ADO method, which was extended to high degree of anisotropy scattering media, this time to solve a radiative heat transfer problem (see Barichello et al 2022), the previous approach failed to provide an appropriate solution, and different approaches were taken to obtain the solution of the system of linear equations that arise in the method.…”

Section: Systems Derived From the Application Of The Ado Methods To A...mentioning

confidence: 99%

“…After writing the one-dimensional transverse-integrated equations in the x and y directions for each region r and using constant functions to properly express the radiation intensities in the contours of a node, we solve two eigenvalue problems to obtain separation constants to describe the homogeneous solutions and finally obtain the equations describing the general solutions for the average intensity along the x and y directions in each node. For details on this derivation, see Barichello et al (2022).…”

Section: Systems Derived From the Application Of The Ado Methods To A...mentioning

confidence: 99%

“…Considering a significant number of discrete directions in the simulations is theoretically recognized as an error control requirement between the discrete ordinate solution and the exact solution (Madsen 1971). Furthermore, from a physical perspective, problems in highly anisotropic scattering media (Barichello et al 2022), for example, also impose such condition which means a choice of high-order quadrature schemes to approximate the integral term of the equation. This is a main factor that directly impacts the linear systems order.…”

Section: Introductionmentioning

confidence: 99%

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On the solution of systems of linear equations associated to the ADO method in particle transport problems

Barichello

Cunha

2023

Comp. Appl. Math.

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In this work, a study is carried out on the solution of large linear systems of algebraic equations relevant to establish a general solution, based on a spectral formulation, to the discrete ordinates approximation of the two-dimensional particle transport equation in Cartesian geometry. The number of discrete ordinates (discrete directions of the particles) is determined by the order of the quadrature scheme on the unity sphere used to approximate the integral term of the linear Boltzmann equation (also called the transport equation). A nodal technique is applied to the discrete ordinates approximation of this equation, yielding to a system of first order ordinary differential equations for average unknowns along the directions x and y. The developed formulation is explicit for the spatial variables. The order of the linear system is defined by the number of discrete directions as well as the number of the spatial nodes. High-quality solutions are expected as both, the number of discrete directions and the refinement of the spatial mesh, increase. Here, the performance of direct and iterative methods, for the solution of the linear systems, are discussed, along with domain decomposition techniques and parallel implementation. Alternative arrangements in the configuration of the equations allowed solutions to higher order systems. A dependence on the type of the quadrature scheme as well as the class of problems to be solved (neutron or radiation problems, for instance) directly affect the final choice of the numerical algorithm.

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Section: Systems Derived From the Application Of The Ado Methods To A...mentioning

confidence: 99%

Section: Systems Derived From the Application Of The Ado Methods To A...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the solution of systems of linear equations associated to the ADO method in particle transport problems

Barichello

Cunha

2023

Comp. Appl. Math.

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“…O método ADO-Nodal já vem sendo utilizado em problemas de transferência radiativa com espalhamento anisotrópico, onde a função de fase é aproximada em termos da expansão truncada de polinômios de Legendre [4]. O presente trabalho propõem uma abordagem para a ETR bidimensional com espalhamento anisotrópico, resolvida pelo método ADO-Nodal, que descreva a função de fase pela forma exata.…”

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Solução ADO para a Equação de Transferência Radiativa em Geometria Bidimensional com a Função de Fase na Forma Exata

Mentges,

Cortelini,

Barichello

et al. 2023

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo Neste trabalho, uma solução para o problema de transferência radiativa em geometria cartesiana bidimensional, com a representação da função de fase na forma exata, é proposta. A formulação utiliza o método ADO-Nodal sendo que diferentemente de trabalhos anteriores, onde expansões truncadas em Polinômios de Legendre eram utilizadas para expressar a função de fase, aqui a mesma é representada pela fórmula exata. Meios com grau de anisotropia arbitrário podem ser considerados. Para justificar a relevância do presente estudo a função de fase de Henyey-Greenstein expandida em polinômios de Legendre é comparada com sua formulação exata. Com isso fica evidenciada a vantagem de utilizar a expansão com valores maiores de L para que o erro entre as duas representações seja menor possível. Resultados numéricos foram obtidos para um problema teste e comparados com a resolução via Método de Diferenças Finitas. A potencialidade do método ADO com a função de fase na forma exata fica indicada uma vez que os resultados obtidos apresentaram concordância satisfatória, redução do tempo computacional e maior generalidade na formulação ADO podendo ser aplicada em diferentes áreas.

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Rotated reference frames in radiative transport theory

Machida

2024

Progress in Optics

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On the application of the ADO method to the solution of two-dimensional radiative transfer problems in anisotropic scattering media

Cited by 6 publications

References 35 publications

On the solution of systems of linear equations associated to the ADO method in particle transport problems

On the solution of systems of linear equations associated to the ADO method in particle transport problems

Solução ADO para a Equação de Transferência Radiativa em Geometria Bidimensional com a Função de Fase na Forma Exata

Rotated reference frames in radiative transport theory

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