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

Thermal transient problems, essential in 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 the application, e. g. for model parameter estimation or online process control. Model order reduction, a solution to preserve accuracy while reducing complexity, is explored. This paper addresses challenges in developing a reduced model 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 examples 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.