A Phase Field Model for Simulating the Freezing of Supercooled Liquid Droplets

In this work, ice accretion is investigated on a fundamental level using a novel Eulerian phase field approach that captures the phase interface. This method, unlike the Allen-Cahn method, does not lead to spurious phase change (artificial mass loss). This method is also straightforward to implement and avoids normal vector reconstructions along the interface or ghost cells. Additionally, it has well-defined and novel stiffness constraints for accuracy and stability that define parameters in the model such as the kinetic coefficient μ and the interface regularization coefficient γ. An incompressible solver is constructed and used to verify the new method using an analytical Stefan problem solution in both 1D and 2D domains.