A volume-of-fluid method for three-dimensional hexagonal solidification processes

A novel volume-of-fluid method to simulate three-dimensional hexagonal solidification processes is presented. The Gibbs-Thomson temperature is calculated using the weighted mean curvature and a height function technique. This boundary condition is applied directly on the sharp interface. A geometric unsplit advection scheme is used to advance the interface to the next timestep. The phase change model is validated against analytical similarity solutions in both two and three dimensions. The influence of the grid resolution on the dendritic growth is studied. Sharper dendrites for increasing resolution were found as a result of the model for the anisotropic surface energy density. Three-dimensional hexagonal growth could be achieved and constrictions were observed in both the basal and prismal planes.