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

Sven Beuchler; Bernhard Endtmayer; Johannes Lankeit; Thomas Wick

doi:10.5802/crmeca.160

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

Sven Beuchler ^1,² ; Bernhard Endtmayer ^1,² ; Johannes Lankeit ¹ ; Thomas Wick ^1,²

¹ Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
² Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines), Leibniz Universität Hannover, Germany

Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 111-133.

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.

Received: 2022-09-10
Revised: 2022-12-09
Accepted: 2022-12-15
Online First: 2023-03-09
Published online: 2024-04-26

DOI: 10.5802/crmeca.160

Keywords: Boussinesq, finite elements, multigoal error control, partition-of-unity dual-weighted residuals, Y-beam splitter

Author's affiliations:

Sven Beuchler ^{1, 2}; Bernhard Endtmayer ^{1, 2}; Johannes Lankeit ¹; Thomas Wick ^{1, 2}

¹ Leibniz Universität Hannover, Institut für Angewandte Mathematik, Welfengarten 1, 30167 Hannover, Germany
² Cluster of Excellence PhoenixD (Photonics, Optics, and Engineering – Innovation Across Disciplines), Leibniz Universität Hannover, Germany

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Sven Beuchler and Bernhard Endtmayer and Johannes Lankeit and Thomas Wick},
     title = {Multigoal-oriented a posteriori error control for heated material processing using a generalized {Boussinesq} model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {111--133},
     publisher = {Acad\'emie des sciences, Paris},
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Sven Beuchler; Bernhard Endtmayer; Johannes Lankeit; Thomas Wick. Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model. Comptes Rendus. Mécanique, Volume 351 (2023) no. S1, pp. 111-133. doi : 10.5802/crmeca.160. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.160/

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