Abstract A lattice Boltzmann-finite volume scheme is proposed to numerically study the equiaxed crystal growth during binary alloy solidification. In present model, the lattice Boltzmann method is extended to numerically model the growth of equiaxed crystal coupled with solute transfer. An anisotropic lattice Boltzmann equation fitting into the lattice Bhatnagar-Gross-Krook (BGK) scheme is applied to describe the liquid-solid phase changes with interfacial anisotropic effect. Solute transfer is described by the diffusion equation including an anti-trapping current term, which is solved by the finite volume scheme and coupled straightly with the anisotropic lattice Boltzmann equation. After model validation, the hybrid model is applied to numerically simulate the equiaxed crystal growth with single and multiple seeds during Al-Cu solidification. The results demonstrate that the hybrid model is an alternative approach for numerical simulations of equiaxed crystal growth during binary alloy solidification with reliable numerical accuracy and excellent computational efficiency, which has important instructional significance for understanding the underlying mechanism of alloy solidification.

中文翻译：

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使用晶格 Boltzmann-有限体积方案对二元合金凝固过程中等轴晶体生长的数值模拟

摘要 为了数值研究二元合金凝固过程中的等轴晶生长，提出了格子Boltzmann-finite体积方案。在目前的模型中，格子玻尔兹曼方法被扩展到数值模拟等轴晶体的生长与溶质转移耦合。应用拟合格子 Bhatnagar-Gross-Krook (BGK) 方案的各向异性格子 Boltzmann 方程来描述具有界面各向异性效应的液固相变化。溶质转移由包含反俘获电流项的扩散方程描述，该方程由有限体积方案求解并与各向异性晶格玻尔兹曼方程直接耦合。模型验证后，混合模型用于数值模拟 Al-Cu 凝固过程中单晶种和多晶种的等轴晶体生长。