Multiphysics simulation of crystal growth with moving boundaries in FEniCS

Crystal growth processes and the Czochralski process in particular involves various physical phenomena such as heat transfer, phase change or liquid flows and requires a coupled multiphysical model for realistic numerical simulations. In this work, a new and extendable model is developed using the open-source software FEniCS. Basic equations for electromagnetic induction, heat conduction and radiation as well as phase change are thoroughly derived up to a finite element form and discussed together with the assumed boundary conditions and approximations. Verification of the FEniCS model with an analytical case demonstrated an accuracy with an error below 1%. A comparison with experimental results and numerical data from a similar model achieved a good agreement and showed opportunities for further improvement of melt flow modeling in particular.