Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods
In this article, we present a methodology to solve radiative transfer problems in spherical geometry without other forms of heat exchange. We use a decomposition method based on the Adomian formulations, together with a diamond difference scheme and a trapezoidal rule to approximate the integral pa...
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| Format: | Article |
| Language: | English |
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Universidade Estadual de Londrina
2024-12-01
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| Series: | Semina: Ciências Exatas e Tecnológicas |
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| Online Access: | https://www.ojs.uel.br/revistas/uel/index.php/semexatas/article/view/51961 |
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| author | Marcelo Schramm Cibele Ladeia Julio Cesar Fernandes |
| author_facet | Marcelo Schramm Cibele Ladeia Julio Cesar Fernandes |
| author_sort | Marcelo Schramm |
| collection | DOAJ |
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In this article, we present a methodology to solve radiative transfer problems in spherical geometry without other forms of heat exchange. We use a decomposition method based on the Adomian formulations, together with a diamond difference scheme and a trapezoidal rule to approximate the integral part of the solution. The algorithm is simple, highly reproducible, and can be easily adapted to further problems or geometries. Also, we demonstrate its consistency and showed that using an analytical solution with a trapezoidal rule improves the order of convergence compared to using the finite difference method. These considerations are necessary for future applications in more complex cases. The numerical results are compared with some classical and recent cases in the literature, along with a simplified version of a complete (fully coupled with heat exchange) case.
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| format | Article |
| id | doaj-art-1020fa280980465195725aa47a6d9892 |
| institution | Kabale University |
| issn | 1676-5451 1679-0375 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Universidade Estadual de Londrina |
| record_format | Article |
| series | Semina: Ciências Exatas e Tecnológicas |
| spelling | doaj-art-1020fa280980465195725aa47a6d98922025-01-17T06:53:19ZengUniversidade Estadual de LondrinaSemina: Ciências Exatas e Tecnológicas1676-54511679-03752024-12-014510.5433/1679-0375.2024.v45.51961Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition MethodsMarcelo Schramm0https://orcid.org/0000-0002-0254-4277Cibele Ladeia1Julio Cesar Fernandes2Universidade Federal de Pelotas Universidade Federal do Rio Grande do Sul Universidade Federal do Rio Grande do Sul In this article, we present a methodology to solve radiative transfer problems in spherical geometry without other forms of heat exchange. We use a decomposition method based on the Adomian formulations, together with a diamond difference scheme and a trapezoidal rule to approximate the integral part of the solution. The algorithm is simple, highly reproducible, and can be easily adapted to further problems or geometries. Also, we demonstrate its consistency and showed that using an analytical solution with a trapezoidal rule improves the order of convergence compared to using the finite difference method. These considerations are necessary for future applications in more complex cases. The numerical results are compared with some classical and recent cases in the literature, along with a simplified version of a complete (fully coupled with heat exchange) case. https://www.ojs.uel.br/revistas/uel/index.php/semexatas/article/view/51961radiativetransferspherical geometrydecomposition methoddiamond differencediscrete ordinates |
| spellingShingle | Marcelo Schramm Cibele Ladeia Julio Cesar Fernandes Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods Semina: Ciências Exatas e Tecnológicas radiativetransfer spherical geometry decomposition method diamond difference discrete ordinates |
| title | Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods |
| title_full | Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods |
| title_fullStr | Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods |
| title_full_unstemmed | Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods |
| title_short | Solution of Linear Radiative Transfer Equation in Hollow Sphere by Diamond Difference Discrete Ordinates and Decomposition Methods |
| title_sort | solution of linear radiative transfer equation in hollow sphere by diamond difference discrete ordinates and decomposition methods |
| topic | radiativetransfer spherical geometry decomposition method diamond difference discrete ordinates |
| url | https://www.ojs.uel.br/revistas/uel/index.php/semexatas/article/view/51961 |
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