Barrett, John W. and Garcke, Harald and Nürnberg, Robert
Numerical computations of facetted pattern formation in snow crystal growth.
Preprintreihe der Fakultät Mathematik 7/2012,
Facetted growth of snow crystals leads to a rich diversity of forms, and exhibits a 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 space dimensions using a new computational method recently introduced by the authors. We present both qualitative and quantitative computations. In particular, a linear relationship between tip velocity and supersaturation is observed. The computations also suggest that surface energy effects, although small, have a larger effect
on crystal growth than previously expected. We compute solid plates, solid prisms, hollow columns, needles, dendrites, capped
columns and scrolls on plates. Although all these forms appear in nature, most of these forms are computed here for the first time in numerical simulations for a continuum model.
|Item Type:||Monograph (Working Paper)|
|Institutions:|| Mathematics > Prof. Dr. Harald Garcke|
|Keywords:||A1. Computer simulation, A1. Crystal morphology, A1. Dendrites, A1. Growth models, A1. Morphological stability, A1.
Solidification, A2. Growth from vapour|
|Subjects:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||19 Mar 2012 07:34|
|Last Modified:||19 Mar 2012 07:34|