Grid anisotropy reduction method for cellular automata based solidification models

The reliability of a cellular automata (CA) simulation for a free dendritic growth problem relies heavily on its ability to reduce the artificial grid anisotropy. Hence, a computationally efficient, accurate and elegant cell capturing methodology is essential to achieve reliable results. Therefore, a novel cell capturing method termed limited circular neighbourhood (LCN) is proposed in the present study for solidification models. The LCN method is applied to the canonical test cases with an isotropic growth rate and is compared with other grid anisotropy reducing methods. It is observed that the LCN method is able to capture the growth orientation accurately. Moreover, the mass loss and shape error in the proposed method is significantly reduced as compared with the other methods. In addition, its performance is also evaluated for a free dendrite growth problem in a pure material in which the growth captured by the LCN method is found to be accurate. Finally, its efficacy is also demonstrated in the results presented for a constrained dendritic growth problem in a binary alloy with multiple growth sites.