A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media
We propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified Pɴ approximations using an asymptotic analysis. T...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| التنسيق: | article |
| منشور في: |
2024
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/11073/26094 |
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إضافة وسم
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| _version_ | 1864513434074218496 |
|---|---|
| author | Belhamadia, Youssef |
| author2 | Seaid, Mohammed |
| author2_role | author |
| author_facet | Belhamadia, Youssef Seaid, Mohammed |
| author_role | author |
| dc.creator.none.fl_str_mv | Belhamadia, Youssef Seaid, Mohammed |
| dc.date.none.fl_str_mv | 2024 2025-06-04T08:01:31Z 2025-06-04T08:01:31Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | Y. Belhamadia, M. Seaid, "A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media", Mathematics and Computers in Simulation, Vol. 216, Pages 15-29, 2024, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2023.08.031. 0378-4754 https://hdl.handle.net/11073/26094 10.1016/j.matcom.2023.08.031 |
| dc.language.none.fl_str_mv | en_US |
| dc.publisher.none.fl_str_mv | Elsevier |
| dc.relation.none.fl_str_mv | https://doi.org/10.1016/j.matcom.2023.08.031 |
| dc.subject.none.fl_str_mv | Radiation–conduction heat transfer Simplified Pɴ approximations Mixed finite element methods Three-dimensional optically thick media |
| dc.title.none.fl_str_mv | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| dc.type.none.fl_str_mv | Published version Peer-Reviewed info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | We propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified Pɴ approximations using an asymptotic analysis. The conductivity is assumed to be nonlinear depending on the temperature along with anisotropic absorption and scattering depending on both the direction and location variables. The simplified Pɴ approximations are enhanced by considering a diffusion tensor capable of describing anisotropic radiative heat transfer. In the present study, we investigate the performance of the unified and mixed formulations combining cubic P₃, quadratic P₂, and linear P₁ finite elements to approximate the temperature in the simplified P₃ model. To demonstrate the performance of the proposed methodology, three-dimensional examples of nonlinear radiation–conduction equations in optically thick anisotropic media are presented. The obtained numerical results demonstrate the accuracy and efficiency of the proposed mixed finite element formulation over the conventional unified finite element formulation to accurately solve the simplified P₃ equations in anisotropic media. |
| format | article |
| id | aus_45c1be94bf935622f1ee76db67894770 |
| identifier_str_mv | Y. Belhamadia, M. Seaid, "A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media", Mathematics and Computers in Simulation, Vol. 216, Pages 15-29, 2024, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2023.08.031. 0378-4754 10.1016/j.matcom.2023.08.031 |
| language_invalid_str_mv | en_US |
| network_acronym_str | aus |
| network_name_str | aus |
| oai_identifier_str | oai:repository.aus.edu:11073/26094 |
| publishDate | 2024 |
| publisher.none.fl_str_mv | Elsevier |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic mediaBelhamadia, YoussefSeaid, MohammedRadiation–conduction heat transferSimplified Pɴ approximationsMixed finite element methodsThree-dimensional optically thick mediaWe propose a new mixed finite element formulation for solving radiation–conduction heat transfer in optically thick anisotropic media. At this optical regime, the integro-differential equations for radiative transfer can be replaced by the simplified Pɴ approximations using an asymptotic analysis. The conductivity is assumed to be nonlinear depending on the temperature along with anisotropic absorption and scattering depending on both the direction and location variables. The simplified Pɴ approximations are enhanced by considering a diffusion tensor capable of describing anisotropic radiative heat transfer. In the present study, we investigate the performance of the unified and mixed formulations combining cubic P₃, quadratic P₂, and linear P₁ finite elements to approximate the temperature in the simplified P₃ model. To demonstrate the performance of the proposed methodology, three-dimensional examples of nonlinear radiation–conduction equations in optically thick anisotropic media are presented. The obtained numerical results demonstrate the accuracy and efficiency of the proposed mixed finite element formulation over the conventional unified finite element formulation to accurately solve the simplified P₃ equations in anisotropic media.Royal Society, UKAmerican University of SharjahElsevier2025-06-04T08:01:31Z2025-06-04T08:01:31Z2024Published versionPeer-Reviewedinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfY. Belhamadia, M. Seaid, "A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media", Mathematics and Computers in Simulation, Vol. 216, Pages 15-29, 2024, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2023.08.031.0378-4754https://hdl.handle.net/11073/2609410.1016/j.matcom.2023.08.031en_UShttps://doi.org/10.1016/j.matcom.2023.08.031oai:repository.aus.edu:11073/260942025-06-04T15:07:18Z |
| spellingShingle | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media Belhamadia, Youssef Radiation–conduction heat transfer Simplified Pɴ approximations Mixed finite element methods Three-dimensional optically thick media |
| status_str | publishedVersion |
| title | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| title_full | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| title_fullStr | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| title_full_unstemmed | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| title_short | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| title_sort | A mixed finite element method for nonlinear radiation–conduction equations in optically thick anisotropic media |
| topic | Radiation–conduction heat transfer Simplified Pɴ approximations Mixed finite element methods Three-dimensional optically thick media |
| url | https://hdl.handle.net/11073/26094 |