Universal dynamics of phase-field models for dendritic growth
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We compare time-dependent solutions of different phase-field models for
dendritic solidification in two dimensions, including a thermodynamically
consistent model and several ad hoc models. The results are identical when the
phase-field equations are operating in their appropriate sharp interface limit.
The long time steady state results are all in agreement with solvability
theory. No computational advantage accrues from using a thermodynamically
consistent phase-field model.