Non-linear simulation of dendritic solidification of an undercooled melt

Two-dimensional finite element simulations of solidification for quiescent undercooled pure metals are presented. The full non-linear, transient heat equation is used with phase front tracking which is subject to local curvature and interfacial kinetics. During early stages of the waveform instability the simulated solutions match the linear stability analysis with fidelity. Beyond the valid range of that analysis the numerical solution continues to demonstrate the physically observed exponential growth behaviour and characteristic spacing between fingers. Whereas the simulations show the sensitivity of dendritic growth to initial conditions, as expected for an unstable process, the overall pattern formation preserves the characteristic spacing. The simulations are terminated after the onset of bifurcation. Thereafter, the numerical model is inappropriate for physical comparison owing to the planar, two-dimensional limitation.

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