Dendritic growth during solidification of pure materials and alloys is a complex multiscale phenomenon that involves phase transition, heat transfer, and melt convection-diffusion. Understanding and quantification of the dendritic growth is critical to determine the formed microstructures and predict macroscopic material properties. This paper presents an improved lattice Boltzmann-phase field (LB-PF) model that can be effectively applied to simulate anisotropic dendritic growth under convection. The main features of the proposed model include the incorporation of the diffuse interface concept in the LB model, and all the processes, including the evolution of the phase-field, the melt convection-diffusion, and the two-phase heat transfer, are modeled using respective LB schemes. It differs from previous hybrid lattice Boltzmann-phase field models in which the LB method is only used for fluid flow and heat transfer while a finite-difference or finite-element based phase-field method is typically applied to model the evolution of the phase field. The intrinsic benefits of the LB method such as simple and explicit algorithms, the capability to handle complex geometry, and the compatibility with parallel computation are thus preserved, and the present LB-PF model also benefits from the diffuse interface treatment that avoids sharp interface tracking. Furthermore, to improve the numerical accuracy and stability, respective multiple-relaxation-time (MRT) LB models are implemented in this framework for all the aforementioned evolution processes. The applicability and accuracy of the present LB-PF model is verified with numerical tests for dendritic growth with both diffusion and melt convection-diffusion conditions.
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