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A Front-Tracking Method for Dendritic Solidification

We present a front-tracking method to simulate time dependent two-dimensional dendritic solidification of pure substances. The method is based on a finite difference approximation of the heat equation and explicit tracking of the liquid?solid interface. Discontinuities in material properties between solid and liquid phases as well as topology changes and interfacial anisotropies are easily handled. The accuracy of the method is verified through comparison with exact solutions to a two-dimensional Stefan problem. Convergence under grid refinement is demonstrated for dendritic solidification problems. Experimentally observed complex dendritic structures such as liquid trapping, tip-splitting, side branching, and coarsening are reproduced. We also show that a small increase in the liquid to solid volumetric heat capacity ratio markedly increases the solid growth rate and interface instability.