During the past two decades, researchers have shown interest in large-scale simulations to analyze alloy solidification. Advances in in situ X-ray observations of the microstructural evolution of dendrites have shown defects that can be very costly for manufacturers. These simulations provide the basis for understanding applied meso-/macro-scale phenomena with microscale details using various numerical schemes to simulate the morphology and solve for transport phenomena. Methods for simulating methodologies include cellular automaton, phase field, direct interface tracking, level set, dendritic needle networks, and Monte Carlo while finite element, finite difference, finite volume, and lattice Boltzmann methods are commonly used to solve for transport phenomena. In this paper, these methodologies are explored in detail with respect to simulating the dendritic microstructure evolution and other solidification-related features. The current research, from innovations in algorithms for scaling to parallel processing details, is presented with a focus on understanding complex real-world phenomena. Topics include large-scale simulations of features with and without convection, columnar to equiaxed transition, dendrite interactions, competitive growth, microsegregation, permeability, and applications such as additive manufacturing. This review provides the framework and methodologies for achieving scalability while highlighting the areas of focus that need more attention.

This paper presents a comparative study between the pseudopotential Shan-Chen model and the phase field multiphase lattice Boltzmann method for simulating bubble dynamics during dendritic solidification of binary alloys. The Shan-Chen method is an efficient lattice Boltzmann multiphase method despite having some limitations, including the generation of large spurious currents. The phase field model solves the Cahn-Hilliard equation in addition to the Navier-Stokes equation to track the interface between phases. The phase field method is more accurate than the Shan-Chen model for simulation of fluids with a high-density ratio since it generates an acceptable small spurious current, though at the expense of higher computational costs. For the simulations in this article, the multiphase lattice Boltzmann model was coupled with the cellular automata and finite difference methods to solve temperature and concentration fields. The simulated results were presented and compared regarding the ability of each model to simulate phenomena at a microscale resolution, such as Marangoni convection, the magnitude of spurious current, and the computational costs. It is shown that although Shan-Chen methods can replicate some qualitative features of bubble-dendrite interaction, the generated spurious current is unacceptably large, particularly for practical values of the density ratio between fluid and gas phases. This occurs even after implementation of several enhancements to the original Shan-Chen method. This serious limitation makes the Shan-Chen models unsuitable to simulate fluid flow phenomena, such as Marangoni convection, because the large spurious currents mask completely the physical flow.

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.