The phase field method has been demonstrated to hold promise for enabling the physics at the microscale to be incorporated in macroscopic models of solidification. However, for quantitatively accurate simulations to be performed, it will be necessary to develop algorithms which enable the interface width to be made very small. Adaptive grid techniques offer a means of achieving this within practical computational limits. This paper investigates the solution of one-dimensional phase field models using an adaptive grid technique. Three problems are considered: (1) the classical Stefan model, (2) the case of a solid sphere in equilibrium with its melt, and (3) a modified Stefan model with a generalized kinetic undercooling term. The numerical results are compared with those obtained using a fixed grid algorithm. In general, the adaptive grid technique is shown to be far more efficient, but it requires some care in its implementation.
Issue Section:
Analytical and Experimental Techniques
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