Publications
Comparative study of different anisotropy and potential formulations of phase-field models for dendritic solidification
J. Kundin, I. Steinbach.
Computational Materials Science, 170, 109197, (2019)
Abstract
Phase-field model formulations with double well and double obstacle potentials, and different anisotropy models
are investigated with respect to their potential to simulate (i) tip growth on a quantitative level, (ii) well resolved
side-branching. The dilute binary alloy Al-4 at%Cu is used as a model alloy. The effects of the numerical re-
solution (the ratio of the capillary length to the grid spacing) on the growth velocity are studied by means of
convergence tests for isothermal and directional solidification in comparison to the theoretical values calculated
by the Green-function method (A. Karma, W.J. Rappel, Phys. Rev. E 57 (1998) 4323). An interface stability
parameter is introduced as a measure for the estimation of the maximum value of the grid spacing for effective
simulations. We show that predominantly the side-branching occurs at numerical resolution lower than the limit
value needed to produce correct results in accordance to the convergence analysis. The best results for dendrite
growth at a relevant numerical resolution are obtained for the double well potential.
Keyword(s): phase-field modelling; dendrite growth; directional solidification; surface anisotropy
DOI: 10.1016/j.commatsci.2019.109197
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