Simulations of Anisotropic Crystal Growth and Interaction with Flow Field Using a Diffuse-Interface Lattice-Boltzmann Formulation

Principal Investigator:
Prof. Dominique Thévenin

Otto von Guericke Universität, Institut für Strömungstechnik und Thermodynamik, Magdeburg, Germany

Local Project ID:

HPC Platform used:
Hawk of HLRS

Date published:


Lattice Boltzmann method (LBM) with phase-field model has been performed to investigate the growth habit of a single ice crystal. Given the multitude of growth habits, pronounced sensitivity to ambient conditions and wide range of scales involved, snowflake crystals are particularly challenging. Only few models are able to reproduce the diversity observed regarding snowflake morphology. It is particularly difficult to perform reliable numerical simulations of snow crystals. Here, we present a modified phase-field model that describes vapor-ice phase transition through anisotropic surface tension, surface diffusion, condensation, and water molecule depletion rate.

Results and Methods

The solver is validated to model snowflake growth under different ambient conditions with respect to humidity and temperature in the plate-growth regime section of the Nakaya diagram. The resulting crystal habits are compared to both numerical and experimental reference data available in the literature[1, 2, 3]. In Fig.1, the overall agreement with experimental data shows that the proposed algorithm correctly captures both the crystal shape and the onset of primary and secondary branching instabilities.

The primary habit of the crystal (six-fold symmetry) is dictated by the anisotropy function (and the microscopic crystallographic structure). At lower supersaturation values where the adsorption rate is slow, the surface diffusion process characteristic time is smaller and therefore dominates over surface adsorption. More explicitly it means that the adsorbed water molecules have enough time to propagate on the crystal surface and find the points with the lowest potential (dictated by the molecules' arrangement in the crystal lattice). Furthermore, given the low growth rate and gradients, the surface is not subject to branching instabilities. As the supersaturation goes up, the larger adsorption rate at the sharper parts of the interface (regions with the highest curvatures and consequently highest surface area) result in the formation of six thick branches (usually referred to as primary branches). In the lower supersaturation regimes these primary branches have a faceted structure following the symmetry of the crystal. As the concentration goes further up, the branches get thinner and rougher (the straight faces tend to disappear); this eventually produces secondary instabilities and branches going towards a somewhat fractal structure. All the obtained crystal habits, are in excellent agreement with not only numerical simulations from [3] but also experimental data from [1]. Further comparing the different crystal habits to Nakaya's diagram, it can be concluded that the proposed model correctly predicts the behavior of the crystal in the platelet regime.

As a next part of the study the effects of forced convection on snowflake growth are studied. Crystal growth subject to ventilation effects reveal that the snow crystal exhibits nonsymmetrical growth. The non-uniform humidity around the snow crystal because of the forced convection can result in different growth rates on different sides of the same crystal. It is shown in Fig.2, in agreement with observations in the literature, that under such conditions the crystal exhibits non-symmetrical growth. The non-uniform humidity around the crystal due to forced convection can even result in the coexistence of different growth modes on different sides of the same crystal.

The simulation domain consists of 5.12 million grid points for the simulation case in Figure 1 and 8 million grid points for the simulation in Figure 2. All the simulation results were calculated up to 57 nodes with 6840 cores, using a total of about 5 million core hours.


[1] Kenneth G. Libbrecht. Snowcrystals. com, 1999. URL, 2005.
[2] Q. Tan, S.A. Hosseini, A. Seidel-Morgenstern, D. Thévenin, and H. Lorenz. Modeling ice crystal growth using the lattice boltzmann method, Physics of Fluids, 341 no. 1, 013311, 2022.
[3] G. Demange, H. Zapolsky, R. Patte, and M. Brunel. A phase field model for snow crystal growth in three dimensions. npj Computational Materials, 3(1):1-7, 2017.