Abstract
When a solidification front is advancing into a region of supercooled liquid, its shape is subject to instabilities which can lead to complex modes of growth. The evaluation of the growth pattern is determined by the interaction of the driving force of the instability due to heat diffusion with the restabilizing force due to surface tension, and its full development is a highly nonlinear process. A new method for solving the two-phase heat diffusion problem under these conditions is described. The method is based on a single-domain treatment (weak formulation) of the moving boundary problem, with the temperature field near the interface approximated by a piecewise linear function in the spirit of the finite-element technique. Calculated results for a model problem are in excellent agreement with the predictions of an analytical approximation.
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