Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion
Variational formulation and numerical accuracy of a quantitative phase-field model for binary alloy solidification with two-sided diffusion
复制标题
双面扩散二元合金凝固定量相场模型的变分公式和数值精度
DOI：
10.1103/physreve.93.012802
复制
发表时间：
2016
影响因子：
2.4
通讯作者：
Y. Shibuta
中科院分区：
文献类型：
--
作者：
M. Ohno;T. Takaki;Y. Shibuta
我们提出了考虑固体扩散的二元稀合金等温低速凝固的定量相场模型的变分公式。在本公式中，相位场和成分场之间的交叉耦合项，包括所谓的反俘获电流，自然会出现在时间演化方程中。本公式中的一个基本成分是利用张量扩散率而不是标量扩散率。在渐近分析中，它表明，本变分模型和自由边界问题的合金凝固与固体扩散率的任意值之间的正确映射成功地实现薄界面的限制，由于交叉耦合项和张量扩散。此外，我们调查的变分模型的数值性能，也通过进行二维模拟自由枝晶生长的非变分版本。具有张量扩散系数的非变分模型显示出相对于界面厚度的结果具有良好的收敛性。
We present the variational formulation of a quantitative phase-field model for isothermal low-speed solidification in a binary dilute alloy with diffusion in the solid. In the present formulation, cross-coupling terms between the phase field and composition field, including the so-called antitrapping current, naturally arise in the time evolution equations. One of the essential ingredients in the present formulation is the utilization of tensor diffusivity instead of scalar diffusivity. In an asymptotic analysis, it is shown that the correct mapping between the present variational model and a free-boundary problem for alloy solidification with an arbitrary value of solid diffusivity is successfully achieved in the thin-interface limit due to the cross-coupling terms and tensor diffusivity. Furthermore, we investigate the numerical performance of the variational model and also its nonvariational versions by carrying out two-dimensional simulations of free dendritic growth. The nonvariational model with tensor diffusivity shows excellent convergence of results with respect to the interface thickness.