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

TL;DR

This paper introduces a multigoal-oriented a posteriori error control method for a coupled Boussinesq model with temperature-dependent properties, enhancing adaptive algorithms for heated material processing simulations.

Contribution

It develops a novel error estimation framework using dual-weighted residuals for coupled thermal-fluid models with temperature-dependent parameters.

Findings

Effective error reduction demonstrated in numerical tests

Robustness of the adaptive method confirmed

High effectivity indices indicate accurate error estimates

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.