VARIATIONAL ALGORITHMS AND PATTERN-FORMATION IN DENDRITIC SOLIDIFICATION

We present a completely new variational algorithm for computing dendritic solidification. This algorithm reproduces the Gibbs-Thomson relation as a balance between bulk and surface energy and is able to operate in the infinite-mobility limit with no unphysical time-step restriction. It may be used with arbitrary non-smooth surface energy functions and may include finite kinetic mobility. We perform computations with isotropic and anisotropic surface energy; from a small irregular initial seed we generate radial tip-splitting structures for isotropic energy and parabolic dendrites with side-branching for anisotropic energy. For anisotropic energy, the final structure is determined by the material and environmental properties; the initial shape is forgotten. For the parabolic dendrite tips, we obtain agreement with the Ivantsov solutions within a few percent and proper dimensional scaling of lengths and velocities with surface energy. © 1993 Academic Press, Inc.