Multiple-relaxation-time lattice Boltzmann model for anisotropic liquid–solid phase change

An extended lattice Boltzmann model is proposed for the anisotropic solidification process based on the quantitative phase-field equation. To include the anisotropy, we derive an equivalent diffusion matrix and design an off-diagonal relaxation-time matrix to recover it within the framework of the lattice Boltzmann method. Different from the standard collision-streaming algorithm, a correction step after the streaming step is introduced, which improves the model's locality. Numerical tests are conducted for the equiaxed dendrite growth in both two and three dimensions. Results obtained by the present lattice Boltzmann model have a good agreement with analytical solution and numerical prediction in literature. Furthermore, the present model shows superiority in efficiency especially for the large-scale modeling in the parallel machines.