论文标题
在树突状晶体生长的3D相场模拟中聚焦潜热释放
Focusing the Latent Heat Release in 3D Phase Field Simulations of Dendritic Crystal Growth
论文作者
论文摘要
我们研究了一个相位场模型家族，用于模拟纯高冷物质的树突生长。感兴趣的中心对象是Allen-CAHN方程中的反应项，该方程负责在凝固过程中潜在热释放的空间分布。在这种情况下，分析了反应项的几种形式。受匹配的渐近分析的已知结论的启发，我们提出了足够简单的新变体，以允许数学和数值分析，并且足够鲁棒，以便在非常大的过冷下适用于凝固。在许多数值模拟中测试了所得模型，该模拟的重点是网格依赖性和模型参数设置。尽管相位界面的厚度相对较大以使数值计算可行，但获得的结果与来自镍熔体快速固化的实验数据表现出了良好的定量一致性。
We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. The central object of interest is the reaction term in the Allen-Cahn equation, which is responsible for spatial distribution of latent heat release during solidification. In this context, several existing forms of the reaction term are analyzed. Inspired by the known conclusions of matched asymptotic analysis, we propose new variants that are simple enough to allow mathematical and numerical analysis and robust enough to be applicable to solidification under very large supercooling. The resulting models are tested in a number of numerical simulations focusing on mesh-dependence and model parameter settings. Despite the phase interface thickness being relatively large to make numerical computations feasible, the obtained results exhibit a good quantitative agreement with experimental data from rapid solidification of nickel melts.
