PGD in thermal transient problems with a moving heat source: A sensitivity study on factors affecting accuracy and efficiency

• Published in: Engineering reports (Hoboken, N.J.) Vol. 6; no. 11
• Main Authors: Strobl, Dominic, Unger, Jörg F., Ghnatios, Chady, Robens‐Radermacher, Annika
• Format: Journal Article
• Language: English
• Published: Hoboken John Wiley & Sons, Inc 01.11.2024; Wiley
• Subjects: Accuracy; additive manufacturing; Algorithms; Boundary conditions; Complex variables; Coordinate transformations; Discretization; Efficiency; Finite difference method; Heat; Heat treatment; Investigations; mapping for unseparable load; Mathematical analysis; Mathematical models; model order reduction (MOR); Model reduction; Parameter estimation; Parameter sensitivity; Process controls; proper generalized decomposition (PGD); Reduced order models; sensitivity analysis; Simulation; thermal transient problem; Thermal transients; Welding parameters
• ISSN: 2577-8196; 2577-8196
• DOI: 10.1002/eng2.12887

Thermal transient problems, essential for modeling applications like welding and additive metal manufacturing, are characterized by a dynamic evolution of temperature. Accurately simulating these phenomena is often computationally expensive, thus limiting their applications, for example for model parameter estimation or online process control. Model order reduction, a solution to preserve the accuracy while reducing the computation time, is explored. This article addresses challenges in developing reduced order models using the proper generalized decomposition (PGD) for transient thermal problems with a specific treatment of the moving heat source within the reduced model. Factors affecting accuracy, convergence, and computational cost, such as discretization methods (finite element and finite difference), a dimensionless formulation, the size of the heat source, and the inclusion of material parameters as additional PGD variables are examined across progressively complex examples. The results demonstrate the influence of these factors on the PGD model's performance and emphasize the importance of their consideration when implementing such models. For thermal example, it is demonstrated that a PGD model with a finite difference discretization in time, a dimensionless representation, a mapping for a moving heat source, and a spatial domain non‐separation yields the best approximation to the full order model. To significantly improve the computational performance of simulations for complex temperature fields, which are often computationally expensive, the proper generalized decomposition method is applied. This article presents and analyses useful tips and tricks to improve the implementation, the convergence, and the overall performance of such a PGD model.