Lattice-Boltzmann scheme for dendritic growth in presence of convection

A composite phase-field/lattice-Boltzmann scheme is proposed to simulate dendritic growth from a supercooled melt. The phase change part of the problem is modelled by the phase-field approach of Karma and Rappel, whereas the flow of the liquid is simulated by the lattice-Boltzmann-BGK (LBGK) method into which interactions with solid and thermal convection are incorporated. Test simulations were performed without convection. The resulting tip velocity, radius and branch pattern were the same as in the finite-difference method of Karma and Rappel. Depending on the level of anisotropy and undercooling, dendrites or doublons were obtained in simulations. Dendritic growth in a shear flow was simulated for different flow velocities as well as the growth in presence of natural thermal convection with different orientations of the crystal in the gravitational field. The influence of parallel flow on the operating state of the tip of the dendrite was investigated. (C) 2004 Elsevier B. V. All rights reserved.