Efficient model for the prediction of dendritic grain growth using the lattice Boltzmann method coupled with a cellular automaton algorithm

Abstract

An efficient model for the prediction of dendritic grain growth is developed coupling the lattice Boltzmann method for solving the transport of solute and a cellular automaton algorithm for determining the evolution of grains’ envelope and the release of solute during phase change. In contrast to solving equations from the field of continuum mechanics the new model is more related to particular occasions what is more similar to the behaviour of cellular automaton algorithms. The resulting dendritic grain growth shows qualitative correctness, although the consideration of solute conservation is still missing. It is shown that neglecting proposed conditions regarding the choice of time step size can destabilize the solid-liquid interface resulting in secondary and ternary dendrite arms.