A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system
A fully-discrete decoupled finite element method for the conserved Allen–Cahn type phase-field model of three-phase fluid flow system
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DOI：
10.1016/j.cma.2021.114376
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发表时间：
2022-02
影响因子：
7.2
通讯作者：
Xiaofeng Yang;Xiaoming He
中科院分区：
文献类型：
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作者：
Xiaofeng Yang;Xiaoming He
在这篇文章中，我们开发和分析了一种新的全离散解耦有限元方法来解决由三个不混溶流体组分组成的系统的流动耦合三元相场模型。基于L2梯度流方法，采用守恒的Allen-Cahn型动力学描述自由界面运动，其中多个非局部型拉格朗日乘子用于精确地保持各相体积守恒.该格式是线性的、二阶时间精度的、无条件能量稳定的，这是由于结合了几种有效的数值技术，包括两步向后差分格式、有限元离散、处理非线性的显式SAV（标量辅助变量）方法和Navier-Stokes方程的投影方法。在每个时间步，非局部分裂技术只需要求解几个解耦的常系数椭圆方程。详细讨论了实施问题。严格证明了该格式的可解性和无条件能量稳定性。大量的二维和三维数值模拟进行了数值验证的准确性，能量稳定性，和所提出的方案的适用性。
In this article, we develop and analyze a novel fully discrete decoupled finite element method to solve a flow-coupled ternary phase-field model for the system consisting of three immiscible fluid components. Based on the L 2-gradient flow approach, the conserved Allen–Cahn type dynamics is used to describe the free interface motion, where multiple nonlocal type Lagrange multipliers are used to accurately conserve the volume of each phase. The scheme is also linear, second-order time accurate, and unconditionally energy stable, due to the combination of several effective numerical techniques, including the two-step backward differentiation scheme, finite element discretization, explicit-SAV (scalar auxiliary variable) method for handling the nonlinearity, and projection method of Navier–Stokes equation. At each time step, the non-local splitting technique only requires solving several decoupled constant-coefficient elliptic equations. The implementation issues are discussed in detail. The solvability and the unconditional energy stability of the scheme are rigorously proved. Plenty of 2D and 3D numerical simulations are carried out to numerically demonstrate the accuracy, energy stability, and applicability of the proposed scheme.