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

Materials Science(all), Mechanics of Materials

Electronic version(s)

https://doi.org/10.5802/crmeca.160 (Access: Open)