Variational Algorithms and Pattern Formation in Dendritic Solidiication
نویسنده
چکیده
We present a completely new variational algorithm for computing den-dritic solidiication. This algorithm reproduces the Gibbs-Thomson relation as a balance between bulk and surface energy, and is able to operate in the innnite-mobility limit with no unphysical time-step restriction. It may be used with arbitrary non-smooth surface energy functions, and may include nite 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-nal 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.
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تاریخ انتشار 1993