Very fast simulation of growth competition between columnar dendritic grains during melt pool solidification

This paper presents a very fast numerical approach to simulate microstructures resulting from melt pool solidification including growth competition of columnar dendritic grains, and equiaxed grains nucleated from the melt. To reduce computation time, an upscaling strategy is proposed, which instead of considering each dendrite individually consists in defining an average solidification front based on physically-informed dendritic growth velocity. The proposed approach also relies on dendritic preferred growth direction, and favorably oriented grain criterion to determine which grain survives the competition. One of the key contribution to significantly reduce the total number of degrees of freedom is to use Voronoi tessellations instead of regular grids for numerical implementation. Results have been compared to experimental data, and to phase field and cellular automaton simulations. Simulated microstructures are similar as those obtained with cellular automaton, while computation cost is dramatically reduced. In addition, a convergence analysis is provided for three-dimensional simulations, with thermal conditions corresponding to metal additive manufacturing to demonstrate how the present work can be used in practice