A phase-field model in two dimensions with surface energy anisotropy is used to simulate dendritic solidification of a pure material from its undercooled melt. The computations are performed using a general purpose adaptive mesh finite-difference algorithm, which was designed to solve coupled sets of nonlinear parabolic partial differential equations. The adaptive computations are compared with a fixed-grid calculation at a dimensionless undercooling of 0.8 using finite-difference schemes developed specifically to solve the phase-field equations. Both algorithms were optimized for vector processors. The comparison is used to discuss the advantages and disadvantages of each approach when used to solve the phase-field equations for the complicated interfacial shapes associated with dendritic solidification. Additionally, the adaptive algorithm is used to simulate dendritic growth for undercoolings as small as 0.1, and results are presented for different values of interface thickness. The results show that a better treatment of the outer boundaries is necessary in order to accurately represent the extent of the thermal field at small undercoolings.
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