A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations
A fractional phase-field model for two-phase flows with tunable sharpness: Algorithms and simulations
复制标题
锐度可调的两相流分数相场模型：算法和模拟
DOI：
10.1016/j.cma.2016.03.018
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发表时间：
2016-06
影响因子：
7.2
通讯作者：
Karniadakis George Em
中科院分区：
文献类型：
--
作者：
Song Fangying;Xu Chuanju;Karniadakis George Em
我们开发了质量守恒的艾伦-卡恩相场模型的分数扩展，该模型描述了两种不可压缩流体的混合物。分数阶控制界面的清晰度，这是典型的扩散在整数阶相场模型。该模型是基于能量变分公式推导的。为了使Allen-Cahn公式保持质量，并与Cahn-Hilliard公式相媲美，但成本较低，采用了一个额外的约束。空间离散化是基于Petrov-Galerkin谱法，而时间离散化是基于稳定的ADI格式对相场方程和Navier-Stokes方程。通过对管道内两相流动和上升气泡的模拟，我们证明了该方法的谱精度，以及控制不同粘度和密度的两种流体之间的界面厚度的能力。我们还证明了使用可变分数阶的公式可以同时处理错误边界效应和界面锐化，而无需额外的分辨率。
We develop a fractional extension of a mass-conserving Allen–Cahn phase field model that describes the mixture of two incompressible fluids. The fractional order controls the sharpness of the interface, which is typically diffusive in integer-order phase-field models. The model is derived based on an energy variational formulation. An additional constraint is employed to make the Allen–Cahn formulation mass-conserving and comparable to the Cahn–Hilliard formulation but at reduced cost. The spatial discretization is based on a Petrov–Galerkin spectral method whereas the temporal discretization is based on a stabilized ADI scheme both for the phase-field equation and for the Navier–Stokes equation. We demonstrate the spectral accuracy of the method with fabricated smooth solutions and also the ability to control the interface thickness between two fluids with different viscosity and density in simulations of two-phase flow in a pipe and of a rising bubble. We also demonstrate that using a formulation with variable fractional order we can deal simultaneously with both erroneous boundary effects and sharpening of the interface at no extra resolution.
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影响因子：
1.8
作者：
J. Guermond;P. Minev
通讯作者：
J. Guermond;P. Minev
影响因子：
3.7
作者：
X. Li;Chuanju Xu;许传炬
通讯作者：
X. Li;Chuanju Xu;许传炬
影响因子：
5.6
作者：
O. Agrawal
通讯作者：
O. Agrawal
影响因子：
3
作者：
L. Evans;H. Soner;P. Souganidis
通讯作者：
L. Evans;H. Soner;P. Souganidis
DOI：
10.1142/9789814360906_0003
发表时间：
2011
期刊：
--
影响因子：
--
作者：
Jie Shen;J. Shen
通讯作者：
Jie Shen;J. Shen