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.

基于定量相场方程，提出了各向异性凝固过程的扩展晶格玻尔兹曼模型。为了包括各向异性，我们推导了一个等效扩散矩阵并设计了一个非对角弛豫时间矩阵以在格子玻尔兹曼方法的框架内恢复它。与标准碰撞流算法不同，在流步骤之后引入了校正步骤，提高了模型的局部性。对二维和三维的等轴枝晶生长进行了数值测试。本格子Boltzmann模型得到的结果与文献中的解析解和数值预测具有很好的一致性。此外，本模型显示出效率优势，特别是对于并行机器中的大规模建模。