A novel phase field method for droplet freezing

Simulations of dynamic freezing of liquid droplets have applications in both natural and industrial processes. In this work, a novel phase field method--based on the accurate conservative diffuse interface method (Jain et al., J. Comput. Phys., 111529, 2022)--is presented for the simulations of droplet freezing and melting. This method is compared against the analytical solutions and the state-of-the-art Allen-Cahn model in two dimensions (2D) based on computational cost, conservation behavior, and accuracy using Stefan problems. Additionally, an order estimate for the interface kinetic coefficient--that is typically arbitrarily chosen--is proposed and verified. A new semi-implicit, iterative time advancement method is presented, which results in a constant coefficient pressure Poisson system for variable density incompressible flows. This method leads to a consistent formulation for the pressure projection method in the presence of phase change. Finally, 2D simulations of droplet impact on a wall and subsequent freezing will be presented.