Thin interface limit of the double-sided phase-field model with convection
Thin interface limit of the double-sided phase-field model with convection
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DOI：
10.1098/rsta.2019.0540
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发表时间：
2020-05-15
期刊：
影响因子：
5
通讯作者：
Varnik, Fathollah
中科院分区：
文献类型：
--
作者：
Subhedar, Amol;Galenko, Peter K.;Varnik, Fathollah
相场模型的薄界面限制扩展到包括通过熔体对流的传输。本分析考虑双面模型（液相和固相的扩散率相等）。对于相场和纳维-斯托克斯方程之间的耦合，使用匹配渐近分析研究了两种常用的方案：(i) 可变粘度和 (ii) 曳力模型。虽然对于变粘度模型，可以在膨胀参数中显示出二阶薄界面极限的存在，但对于曳力模型来说，满足二阶无滑移边界条件会出现困难。然而，详细的二维数值模拟表明，在两种耦合方案获得的强制熔体流动存在的情况下，枝晶生长曲线实际上没有差异。这表明这两种方法都可以用于数值模拟的目的。模拟结果还与解析理论进行了比较，显示出弱流的良好一致性。根据基本理论假设讨论较高流体速度下的偏差。本文是主题“软物质和生物物质中的模式”的一部分。
The thin interface limit of the phase-field model is extended to include transport via melt convection. A double-sided model (equal diffusivity in liquid and solid phases) is considered for the present analysis. For the coupling between phase-field and Navier-Stokes equations, two commonly used schemes are investigated using a matched asymptotic analysis: (i) variable viscosity and (ii) drag force model. While for the variable viscosity model, the existence of a thin interface limit can be shown up to the second order in the expansion parameter, difficulties arise in satisfying no-slip boundary condition at this order for the drag force model. Nevertheless, detailed numerical simulations in two dimensions show practically no difference in dendritic growth profiles in the presence of forced melt flow obtained for the two coupling schemes. This suggests that both approaches can be used for the purpose of numerical simulations. Simulation results are also compared to analytic theory, showing excellent agreement for weak flow. Deviations at higher fluid velocities are discussed in terms of the underlying theoretical assumptions.This article is part of the theme issue 'Patterns in soft and biological matters'.