Details
| Original language | English |
|---|---|
| Pages (from-to) | 1-23 |
| Number of pages | 23 |
| Journal | Comptes Rendus - Mecanique |
| Volume | 351 |
| Early online date | 9 Mar 2023 |
| Publication status | Published - 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.
Keywords
- Boussinesq, finite elements, multigoal error control, partition-of-unity dual-weighted residuals, Y-beam splitter
ASJC Scopus subject areas
- Materials Science(all)
- General Materials Science
- Engineering(all)
- Mechanics of Materials
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In: Comptes Rendus - Mecanique, Vol. 351, 26.04.2024, p. 1-23.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Multigoal-oriented a posteriori error control for heated material processing using a generalized Boussinesq model
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.
PY - 2024/4/26
Y1 - 2024/4/26
N2 - 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.
AB - 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.
KW - Boussinesq
KW - finite elements
KW - multigoal error control
KW - partition-of-unity dual-weighted residuals
KW - Y-beam splitter
UR - http://www.scopus.com/inward/record.url?scp=85152669528&partnerID=8YFLogxK
U2 - 10.5802/crmeca.160
DO - 10.5802/crmeca.160
M3 - Article
AN - SCOPUS:85152669528
VL - 351
SP - 1
EP - 23
JO - Comptes Rendus - Mecanique
JF - Comptes Rendus - Mecanique
SN - 1631-0721
ER -