Reduced order models for welding and solidification processes

This paper reviews the foundations of modelling of materials processing and methodologies of analysis outside the traditional discretization of the domain (e.g. finite elements, finite volume, etc.). It starts with a review of the mathematical framework with a focus on dimensional analysis and characteristic values. The methodology of minimal representation and correction factor is discussed with emphasis on computational methods to obtain the minimal representation and on the methodology of blending to obtain the correction factors. Welding on a thin plate with surface heat losses is used as a case study, and the results obtained are validated against published data for many materials, processes, and researchers.