Phase-field lattice Boltzmann simulation of three-dimensional settling dendrite with natural convection during nonisothermal solidification of binary alloy

Understanding the motion and growth behaviors of equiaxed dendrites during solidification is important for predicting macrosegregation. In this study, we develop a phase-field lattice Boltzmann (PF-LB) simulation method for the settling and growth of an equiaxed dendrite during the nonisothermal solidification of a binary alloy. The PF-LB computations are accelerated by employing parallel computation using multiple graphic processing units (GPUs) and the octree block-structured adaptive mesh refinement method, which incorporates multiple mesh and time increment methods. By using the developed method, we can simulate the three-dimensional long-distance settling dendrite while considering the effects of latent heat release and natural convection. From the simulation results, we confirm that the natural convection due to the high solute concentration around a dendrite reduces the settling velocity. In addition, we observe that the temperature increase owing to latent heat release slows dendrite growth, which in turn slightly slows the settling velocity. From these results, we confirm that the effects of latent heat release and natural convection are not negligible in the quantitative evaluation of settling dendrites.