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The Navier–Stokes–Cahn–Hilliard model with a high-order polynomial free energy
Acta Mechanica ( IF 2.7 ) Pub Date : 2020-04-02 , DOI: 10.1007/s00707-020-02666-y
Jaemin Shin , Junxiang Yang , Chaeyoung Lee , Junseok Kim

In this paper, we present a high-order polynomial free energy for the phase-field model of two-phase incompressible fluids. The model consists of the Navier–Stokes (NS) equation and the Cahn–Hilliard (CH) equation with a high-order polynomial free energy potential. In practice, a quartic polynomial has been used for the bulk free energy in the CH equation. It is well known that the CH equation does not satisfy the maximum principle and the phase-field variable takes shifted values in the bulk phases instead of taking the minimum values of the double-well potential. This phenomenon substantially changes the original volume enclosed by the isosurface of the phase-field function. Furthermore, it requires fine resolution to keep small shapes. To overcome these drawbacks, we propose high-order (higher than fourth order) polynomial free energy potentials. The proposed model is tested for an equilibrium droplet shape in a spherical symmetric configuration and a droplet deformation under a simple shear flow in a fully three-dimensional fluid flow. The computational results demonstrate the superiority of the proposed model with a high-order polynomial potential to the quartic polynomial function in volume conservation property.

中文翻译:

具有高阶多项式自由能的 Navier-Stokes-Cahn-Hilliard 模型

在本文中,我们提出了两相不可压缩流体的相场模型的高阶多项式自由能。该模型由具有高阶多项式自由能势的 Navier-Stokes (NS) 方程和 Cahn-Hilliard (CH) 方程组成。实际上,四次多项式已用于 CH 方程中的体自由能。众所周知,CH方程不满足最大值原理,相场变量在体相中取移位值,而不是取双阱电位的最小值。这种现象显着改变了由相场函数的等值面包围的原始体积。此外,它需要精细的分辨率来保持小形状。为了克服这些缺点,我们提出了高阶(高于四阶)多项式自由能势。所提出的模型在球对称配置中的平衡液滴形状和完全三维流体流中的简单剪切流下的液滴变形进行了测试。计算结果证明了所提出的具有高阶多项式势的模型在体积守恒性质上优于四次多项式函数。
更新日期:2020-04-02
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