Stability of numerical simulations of dendritic solidification

Novel developments in the numerical simulation of diffusion limited dendritic growth are discussed in the context of two-dimensional simulations of solidification of pure substances and of binary alloys. The three most important numerical difficulties encountered in the simulations of dendritic growth of binary alloys are discussed : 1) the need to accurately calculate the position and velocity of the interface as part of the solution; 2) the disparity of length scales between the thermal diffusion length and the solute diffusion length ; and 3) the instability of the solid-liquid interface, particularly at high concentrations of solute. Dealing with the third difficulty constitutes the main objective of this paper. The stability of calculations is studied using the continuity condition on the heat flux across the interface and numerical simulations. The latter are used to assess the current modeling capabilities and the hurdles faced to produce more powerful simulators.