Phase-field lattice Boltzmann method with two-relaxation-time model for dendrite growth of a binary alloy with melt convection

To perform accurate, stable, and efficient phase-field lattice Boltzmann (PF-LB) simulations of the solidification of alloys with melt convection, a two-relaxation-time (TRT) model for calculating the collision term in the LB equation and an interpolated bounce-back (IBB) model for imposing a non-slip condition at a solid-liquid interface—(TRT-IBB model)—were introduced. The simulations of the plane Poiseuille flow and the dendrite growth of a binary alloy with forced convection were performed to confirm the computational accuracy and acceleration of PF-LB simulations upon introducing the TRT-IBB model. For dendrite growth with forced convection, the simulations of the TRT-IBB model were in good agreement with those of the conventional single-relaxation-time (SRT) model and the dissipative drag force (DDF) model for imposing the non-slip condition at the diffuse interface (SRT-DDF model). In addition, this study confirmed that the TRT-IBB model enabled stable simulations with ~500-times larger time increment than the SRT-DDF model. Thus, the developed TRT-IBB model was found to be extremely effective in the acceleration of PF-LB simulations for the solidification of alloys with melt convection. © 2020 Elsevier B.V.