Mathematical Modeling and Numerical Simulation of Freezing Processes of a Supercooled Melt under Consideration of Density Changes

In this paper, we derive a model for the two-phase freezing process of supercooled uids. Especially, we take density changes along the phase interfaces into account. Thus, besides heat diiusion and the interface phenomena, mass transport and convection in the uid phase which is given by the full Navier{Stokes equations has to be considered. For the 2D case we implemented an algorithm for the numerical solution of the mathematical model using uniform volume cells for a nite diierence discretization. Additionally, the phase boundaries are captured by a surface tracking method. We report on the mathematical model and its derivation, describe the numerical algorithm and present numerical experiments.