发表机构
Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对热溶质枝晶凝固中多时间尺度问题，提出统一多速率多松弛时间格子玻尔兹曼方法，通过分离源项并即时传递相变贡献，实现稳定模拟，再现枝晶形态并公开代码。
AI 中文摘要
热溶质枝晶凝固涉及界面演化、溶质扩散、传热和熔体流动，这些过程的时间尺度差异显著。在格子玻尔兹曼模拟中，单一数值时间间隔可能使不同的输运过程处于不利的松弛范围内，而异步更新则需要一致地传递相变贡献。为解决这些问题，开发了一种统一的多速率多松弛时间格子玻尔兹曼方法，用于热、溶质和热溶质枝晶凝固。耦合场共享共同的矩空间框架，但以不同的更新速率演化。浓度和温度源项被分离为与输运相关的贡献和相变贡献，每个已解析的相增量用于立即传递相应的溶质和潜热贡献。该方法在纯扩散和强制对流条件下再现了特征性的枝晶形态和尖端速度趋势，对测试的更新因子敏感性较弱。在刘易斯数 \\(Le=1\\)--\\(1000\\) 范围内的定向凝固捕获了从近平面对细胞状和强分支生长的转变，包括垂直排列的枝晶和盐水中的富溶质枝晶间通道，与实验定性一致。源耦合消融实验表明，随着时间尺度分离的增加，延迟的粗步传递会产生越来越强的局部源脉冲，并最终导致数值稳定性丧失，而相步瞬时传递在测试条件下保持稳定。这些结果证明了所提出框架对具有强分离输运时间尺度的枝晶凝固的适用性。源代码公开在\emph{DendriteLBM}存储库中。
英文摘要
Thermosolutal dendritic solidification involves interface evolution, solute diffusion, heat transfer, and melt flow over markedly different time scales. In lattice Boltzmann simulations, a single numerical time interval may place different transport processes in unfavorable relaxation ranges, while asynchronous updates require consistent transfer of phase-change contributions. To address these issues, a unified multirate multiple-relaxation-time lattice Boltzmann method is developed for thermal, solutal, and thermosolutal dendritic solidification. The coupled fields share a common moment-space framework but evolve at different update rates. The concentration and temperature source terms are separated into transport-related and phase-change contributions, and each resolved phase increment is used to immediately transfer the corresponding solutal and latent-heat contributions. The method reproduces characteristic dendritic morphologies and tip-velocity trends under pure diffusion and forced convection, with weak sensitivity to the tested update factors. Directional solidification over Lewis numbers \(Le=1\)--\(1000\) captures the transition from nearly planar to cellular and strongly branched growth, including vertically aligned dendrites and solute-rich interdendritic channels for saline water, in qualitative agreement with experiments. Source-coupling ablation shows that delayed coarse-step transfer produces increasingly strong local source pulses and eventual loss of numerical stability as time-scale separation increases, whereas phase-step instantaneous transfer remains stable over the tested conditions. These results demonstrate the applicability of the proposed framework to dendritic solidification with strongly separated transport time scales. The source code is publicly available in the \emph{DendriteLBM} repository.
Comments19 pages, 12 figures
