Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model
In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a mo...
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| Language: | English |
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Académie des sciences
2023-03-01
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| Series: | Comptes Rendus. Mécanique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.160/ |
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| author | Beuchler, Sven Endtmayer, Bernhard Lankeit, Johannes Wick, Thomas |
| author_facet | Beuchler, Sven Endtmayer, Bernhard Lankeit, Johannes Wick, Thomas |
| author_sort | Beuchler, Sven |
| collection | DOAJ |
| description | In this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework. |
| format | Article |
| id | doaj-art-eaa56f1b50f6469b8a9bf9da262a593b |
| institution | Kabale University |
| issn | 1873-7234 |
| language | English |
| publishDate | 2023-03-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mécanique |
| spelling | doaj-art-eaa56f1b50f6469b8a9bf9da262a593b2025-02-07T13:46:20ZengAcadémie des sciencesComptes Rendus. Mécanique1873-72342023-03-01351S111113310.5802/crmeca.16010.5802/crmeca.160Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq modelBeuchler, Sven0https://orcid.org/0000-0001-9411-8701Endtmayer, Bernhard1https://orcid.org/0000-0003-0647-7371Lankeit, Johannes2https://orcid.org/0000-0002-2563-7759Wick, Thomas3https://orcid.org/0000-0002-1102-6332Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines), Leibniz Universität Hannover, Germany; Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, GermanyCluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines), Leibniz Universität Hannover, Germany; Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, GermanyLeibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, GermanyCluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines), Leibniz Universität Hannover, Germany; Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, GermanyIn this work, we develop a posteriori error control for a generalized Boussinesq model in which thermal conductivity and viscosity are temperature-dependent. Therein, the stationary Navier–Stokes equations are coupled with a stationary heat equation. The coupled problem is modeled and solved in a monolithic fashion. The focus is on multigoal-oriented error estimation with the dual-weighted residual method in which an adjoint problem is utilized to obtain sensitivity measures with respect to several goal functionals. The error localization is achieved with the help of a partition-of-unity in a weak formulation, which is specifically convenient for coupled problems as we have at hand. The error indicators are used to employ adaptive algorithms, which are substantiated with several numerical tests such as one benchmark and two further experiments that are motivated from laser material processing. Therein, error reductions and effectivity indices are consulted to establish the robustness and efficiency of our framework.https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.160/Boussinesqfinite elementsmultigoal error controlpartition-of-unity dual-weighted residualsY-beam splitter |
| spellingShingle | Beuchler, Sven Endtmayer, Bernhard Lankeit, Johannes Wick, Thomas Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model Comptes Rendus. Mécanique Boussinesq finite elements multigoal error control partition-of-unity dual-weighted residuals Y-beam splitter |
| title | Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model |
| title_full | Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model |
| title_fullStr | Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model |
| title_full_unstemmed | Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model |
| title_short | Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model |
| title_sort | multigoal oriented a posteriori error control for heated material processing using a generalized boussinesq model |
| topic | Boussinesq finite elements multigoal error control partition-of-unity dual-weighted residuals Y-beam splitter |
| url | https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.160/ |
| work_keys_str_mv | AT beuchlersven multigoalorientedaposteriorierrorcontrolforheatedmaterialprocessingusingageneralizedboussinesqmodel AT endtmayerbernhard multigoalorientedaposteriorierrorcontrolforheatedmaterialprocessingusingageneralizedboussinesqmodel AT lankeitjohannes multigoalorientedaposteriorierrorcontrolforheatedmaterialprocessingusingageneralizedboussinesqmodel AT wickthomas multigoalorientedaposteriorierrorcontrolforheatedmaterialprocessingusingageneralizedboussinesqmodel |