Simulation of Dendritic Growth with Different Orientation by Using the Point Automata Method

The aim of this paper is simulation of thermally induced liquid-solid dendritic growth in two dimensions by a coupled deterministic continuum mechanics heat 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 information from the deterministic model and the deterministic model receives the solid fraction information from the stochastic model. The heat transfer model is solved on a regular grid by the standard explicit Finite Difference Method (FDM). The phase-change kinetics model is solved by the classical Cellular Automata (CA) approach and a novel Point Automata (PA) approach. The PA method was developed and introduced in this paper to circumvent the mesh anisotropy problem, associated with the classical 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 is established on quadratic cells and Neumann neighborhood. The PA approach is established on randomly distributed points and neighbourhood 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 comprehensive comparison between both stochastic approaches has been made with respect to curvature calculations, dendrites with different orientations of crystallographic angles and types of the node arrangements randomness. It has been shown that the new method can be used for calculation of the dendrites in any direction.

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