Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autoren

  • Sven Beuchler
  • Bernhard Endtmayer
  • Johannes Lankeit
  • Thomas Wick
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Details

OriginalspracheEnglisch
Seiten (von - bis)1-23
Seitenumfang23
FachzeitschriftComptes Rendus - Mecanique
Jahrgang351
Frühes Online-Datum9 März 2023
PublikationsstatusVeröffentlicht - 26 Apr. 2024

Abstract

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.

ASJC Scopus Sachgebiete

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Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model. / Beuchler, Sven; Endtmayer, Bernhard; Lankeit, Johannes et al.
in: Comptes Rendus - Mecanique, Jahrgang 351, 26.04.2024, S. 1-23.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Beuchler S, Endtmayer B, Lankeit J, Wick T. Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model. Comptes Rendus - Mecanique. 2024 Apr 26;351:1-23. Epub 2023 Mär 9. doi: 10.5802/crmeca.160
Beuchler, Sven ; Endtmayer, Bernhard ; Lankeit, Johannes et al. / Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model. in: Comptes Rendus - Mecanique. 2024 ; Jahrgang 351. S. 1-23.
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abstract = "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.",
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AU - Beuchler, Sven

AU - Endtmayer, Bernhard

AU - Lankeit, Johannes

AU - Wick, Thomas

N1 - Funding Information: Funding. This work has been supported by the Cluster of Excellence PhoenixD (EXC 2122, Project ID 390833453). The second author is supported by an Humboldt Postdoctoral Fellowship.

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