Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth,Advanced Theory and Simulations

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Solution to Multiscale and Multiphysics Problems: A Phase‐Field Study of Fully Coupled Thermal‐Solute‐Convection Dendrite Growth
Advanced Theory and Simulations ( IF 2.9 ) Pub Date : 2021-02-11 , DOI: 10.1002/adts.202000251
Ang Zhang _{1,

2} , Bin Jiang ₁ , Zhipeng Guo ₃ , Jinglian Du ₂ , Qigui Wang ₄ , Fusheng Pan ₁ , Shoumei Xiong _{2,

5}

Affiliation

Solidification process is a complex phase transition problem involving multiscale and multiphysical characteristics. To investigate the complex interaction, a high‐performance numerical scheme is developed to explore the thermal‐solute‐convection interaction during solidification. Al–Cu dendrite growth with the Lewis number ≈10⁴ and Prandtl number ≈10⁻² (or Schmidt number ≈10²) is simulated and discussed. By constructing a multilevel data structure, this numerical scheme allows the time step magnified by 2–3 orders of magnitude in comparison with that for explicit methods. With the capacity of the acceleration strategy including parallel computing and adaptive mesh refinement, the computing efficiency can be further improved by 2–3 orders of magnitude. The combination of multilevel structure and acceleration strategy makes a problem of up to 10⁹ uniform meshes much easier to handle. The coupled governing equations involving the multiscale and multiphysical characteristics are solved with high efficiency and high numerical stability, even when the solid fraction approaches 100%. Both single and multi‐dendrite growths are discussed to reveal the effect of the thermal‐solute‐convection interaction on the large‐scale 2D and 3D microstructure evolution. The presence of the liquid flow changes the distribution of both domain temperature and solute component, which changes dendrite morphology and growth dynamics.

中文翻译：

解决多尺度和多物理场问题：全耦合热溶质对流枝晶生长的相场研究

凝固过程是一个复杂的相变问题，涉及多尺度和多物理特性。为了研究复杂的相互作用，开发了一种高性能的数值方案来研究凝固过程中的热-固-对流相互作用。Al-Cu系的枝晶生长与路易斯数≈10 ⁴和普朗特数≈10 ^-2（或Schmidt数≈10 ²）进行了模拟和讨论。通过构造多级数据结构，与显式方法相比，此数值方案可以将时间步长放大2–3个数量级。借助包括并行计算和自适应网格细化在内的加速策略的能力，计算效率可以进一步提高2-3个数量级。多层次结构和加速策略的结合使问题最多达到10 ⁹均匀的网格更易于处理。即使固体分数接近100％，也可以高效，高数值稳定性地解决涉及多尺度和多物理特性的耦合控制方程。讨论了单枝晶和多枝晶的生长，以揭示热固溶对流相互作用对大型2D和3D微结构演化的影响。液体流的存在改变了畴温度和溶质组分的分布，这改变了枝晶形态和生长动力学。

更新日期：2021-03-09

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