In this paper, we present the ability of the Lattice Boltzmann (LB) equation,
usually applied to simulate fluid flows, to simulate various shapes of
crystals. Crystal growth is modeled with a phase-field model for a pure
substance, numerically solved with a LB method in 2D and 3D. This study focuses
on the anisotropy function that is responsible for the anisotropic surface
tension between the solid phase and the liquid phase. The anisotropy function
involves the unit normal vectors of the interface, defined by gradients of
phase-field. Those gradients have to be consistent with the underlying lattice
of the LB method in order to avoid unwanted effects of numerical anisotropy.
Isotropy of the solution is obtained when the directional derivatives method,
specific for each lattice, is applied for computing the gradient terms. With
the central finite differences method, the phase-field does not match with its
rotation and the solution is not any more isotropic. Next, the method is
applied to simulate simultaneous growth of several crystals, each of them being
defined by its own anisotropy function. Finally, various shapes of 3D crystals
are simulated with standard and non standard anisotropy functions which favor
growth in -, - and -directions