Técnicas de Matriz Resposta com Aproximações de Baixa Ordem Aplicadas a Problemas de Transporte de Fótons

Iram Barbaro Rivas Ortiz; Susana Marrero Iglesias; Francisco Bruno Souza Oliveira; Paulo Eduardo Ambrósio; Dany Sanchez Dominguez

doi:10.14295/vetor.v33i2.16440

Authors

Iram Barbaro Rivas Ortiz UESC https://orcid.org/0000-0001-6917-0102
Susana Marrero Iglesias Programa de Pós-Graduação em Modelagem Computacional em Ciência e Tecnologia – Universidade Estadual de Santa Cruz
Francisco Bruno Souza Oliveira Programa de Pós-Graduação em Modelagem Computacional em Ciência e Tecnologia – Universidade Estadual de Santa Cruz https://orcid.org/0000-0002-9847-7290
Paulo Eduardo Ambrósio Programa de Pós-Graduação em Modelagem Computacional em Ciência e Tecnologia – Universidade Estadual de Santa Cruz https://orcid.org/0000-0002-6043-3591
Dany Sanchez Dominguez Programa de Pós-Graduação em Modelagem Computacional em Ciência e Tecnologia – Universidade Estadual de Santa Cruz https://orcid.org/0000-0002-0640-2970

DOI:

https://doi.org/10.14295/vetor.v33i2.16440

Keywords:

Response Matrix Spectral Nodal Methods, Discrete Ordinate Formulation, Radiative Transfer

Abstract

Radiative transfer and photon transport problems are frequently encountered in various fields of science and engineering, ranging from computerized tomography and radiotherapy to astrophysics, non-destructive testing of materials, radiological protection, among other domains. Challenges persist in this field, including the need for more accurate and comprehensive data, the incorporation of more realistic and complex geometries, and the development of efficient algorithms to solve the photon transport equation as a mathematical model. This work introduces approaches that employ response matrix techniques with low-order approximations to address problems related to photon transport. Specifically, the Response Matrix - Nodal Constant (RM-CN) and Response Matrix - Full Linear Nodal (RM-FLN) methods are presented, considering the isotropic phase function in Cartesian two-dimensional geometry, gray atmosphere, and the discrete ordinates (S_N) formulation of the photon transport equation. The performance of the methods is evaluated in terms of accuracy by solving a model problem. Both response matrix methods generate accurate results for coarse spatial discretization grids, with the best results reported by the RM-FLN method. However, the computational cost is higher when compared to the RM-CN method for the same spatial discretization grid. Finally, the discrete ordinates formulation correctly models the wave effects generated between the absorbing regions of the problem, and ray effects are mitigated as the angular order of the formulation increases.

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