SOLUTION OF DENDRITIC GROWTH IN A BINARY ALLOY BY A NOVEL POINT AUTOMATA METHOD

The aim of this paper is simulation of thermally induced liquid-solid dendritic growth in a binary alloy (Fe-0.6%C) steel in two dimensions by a coupled deterministic continuum mechanics heat and species transfer model and a stochastic localized phase change kinetics model that takes into account the undercooling, curvature, kinetic, and thermodynamic anisotropy. The stochastic model receives temperature and concentration information from the deterministic model and the deterministic heat and species diffusion equations receive the solid fraction information from the stochastic model. The heat and species transfer models are solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by the novel Point Automata (PA) approach. The PA method was developed and introduced [1,2] in order to circumvent the mesh anisotropy problem, associated with the classical Cellular Automata (CA) method. Dendritic structures are in the CA approach sensitive on the relative angle between the cell structure and the preferential crystal growth direction which is not physical. The CA approach used in the paper for reference comparison is established on quadratic cells and Neumann neighborhood. The PA approach is established on randomly distributed points and neighborhood configuration, similar as appears in meshless methods. Both methods provide same results in case of regular PA node arrangements and neighborhood configuration with five points. A comparison between both stochastic approaches has been made with respect to dendritic growth with different orientations of crystallographic angles. It is demonstrated that the new PA method can cope with dendritic growth of a binary alloy in any direction which is not the case with the CA method.