Reduced order methods for the solution of solidification Phase-Field models

Solidification processes are present in a wide range of manufacturing methods and applications, from metallurgy to food processing. In recent years, Phase Field models have been increasingly used to simulate and predict the formation and evolution of material microstructure and phase change interfacial kinetics. However, these methods usually lead to computationally involved numerical schemes, revealing the need for more efficient computational solutions. In this work, two different model reduction techniques, the Laplacian Spectral Decomposition and the Proper Orthogonal Decomposition, have been employed for model reduction of the Kobayashi model, a non-linear solidification Phase-field model. The performance of both low-order models has been illustrated and compared using a range of undercooling and seeding conditions. Results obtained accurately represent the behaviour of the full system, showing the potential of reduced order approaches for the modelling of complex interfacial systems.