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

authored by
Sven Beuchler, Bernhard Endtmayer, Johannes Lankeit, Thomas Wick
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.

Organisation(s)
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
Institute of Applied Mathematics
Type
Article
Journal
Comptes Rendus - Mecanique
Volume
351
Pages
1-23
No. of pages
23
ISSN
1631-0721
Publication date
26.04.2024
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
General Materials Science, Mechanics of Materials
Electronic version(s)
https://doi.org/10.5802/crmeca.160 (Access: Open)