A Front-Tracking Method for Dendritic Solidification

simulations of morphological instabilities and dendritic solidification is given first, in order to put our work into perWe present a front-tracking method to simulate time dependent two-dimensional dendritic solidification of pure substances. The spective. method is based on a finite difference approximation of the heat The process of solidification of a pure substance can equation and explicit tracking of the liquid–solid interface. Discontioccur in either a stable or an unstable manner. Stable nuities in material properties between solid and liquid phases as solidification, classically called the Stefan problem, is charwell as topology changes and interfacial anisotropies are easily acterized by conduction of heat away from the solid–liquid handled. The accuracy of the method is verified through comparison with exact solutions to a two-dimensional Stefan problem. Converinterface through the solid. The interface generally remains gence under grid refinement is demonstrated for dendritic solidifismooth; any protrusions of the solid into the liquid are cation problems. Experimentally observed complex dendritic strucretarded. Stable solidification is dominated by heat diffutures such as liquid trapping, tip-splitting, side branching, and sion while surface tension and interface kinetic effects are coarsening are reproduced. We also show that a small increase in negligible. Analytic solutions of the Stefan problem for the liquid to solid volumetric heat capacity ratio markedly increases simple geometries are well known (see, for example, [1]). the solid growth rate and interface instability. Q 1996 Academic