Numerical computations of faceted pattern formation in snow crystal growth

Faceted growth of snow crystals leads to a rich diversity of forms with remarkable sixfold symmetry. Snow crystal structures result from diffusion-limited crystal growth in the presence of anisotropic surface energy and anisotropic attachment kinetics. It is by now well understood that the morphological stability of ice crystals strongly depends on supersaturation, crystal size, and temperature. Until very recently it was very difficult to perform numerical simulations of this highly anisotropic crystal growth. In particular, obtaining facet growth in combination with dendritic branching is a challenging task. We present numerical simulations of snow crystal growth in two and three spacial dimensions using a computational method recently introduced by the present authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. In our computations, surface energy effects, although small, have a pronounced effect on crystal growth. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped columns, and scrolls on plates. Although all these forms appear in nature, it is a significant challenge to reproduce them with the help of numerical simulations for a continuum model.