Fully discrete, decoupled and energy-stable Fourier-Spectral numerical scheme for the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy flow regime of two-phase incompressible flows
Fully discrete, decoupled and energy-stable Fourier-Spectral numerical scheme for the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy flow regime of two-phase incompressible flows
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DOI：
10.1016/j.cma.2023.116289
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发表时间：
2023-10
影响因子：
7.2
通讯作者：
Shilin Zeng;Ziqing Xie;X. Yang;Jiangxin Wang
中科院分区：
文献类型：
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作者：
Shilin Zeng;Ziqing Xie;X. Yang;Jiangxin Wang
在本文中，我们引入完全离散傅里叶谱数值格式来求解与纳维-斯托克斯/达西方程相结合的非局部卡恩-希利亚德方程，该方程代表自由流态或赫勒-肖单元中两相不可压缩流动的相场模型。该方案通过结合离散非线性势的标量辅助变量（SAV）方法和处理耦合非线性平流/表面张力项的“零能量贡献”（ZEC）方法，实现了完全解耦，同时保持了线性和能量稳定性。该方案的效率归因于其线性解耦结构以及它只需要在每个时间步求解几个具有常系数的椭圆方程。我们严格建立该方案的无条件能量稳定性。此外，还提供了一些 2D 和 3D 数值模拟，以显示其有效性，包括其准确性、稳定性和效率。
In this paper, we introduce fully discrete Fourier-Spectral numerical scheme to solve the nonlocal Cahn–Hilliard equation coupled with Navier–Stokes/Darcy equations, which represent a phase-field model for two-phase incompressible flow in either the free flow regime or a Hele-Shaw cell. The proposed scheme achieves full decoupling while maintaining linearity and energy stability through a combination of the Scalar Auxiliary Variable (SAV) method, which discretizes the nonlinear potential, and the “Zero-Energy-Contribution” (ZEC) method, which handles the coupled nonlinear advective/surface tension terms. The efficiency of this scheme is attributed to its linear decoupling structure and the fact that it requires only a few elliptic equations with constant coefficients to be solved at each time step. We rigorously establish the scheme’s unconditional energy stability. Further, some numerical simulations are provided in both 2D and 3D to show its effectiveness, including its accuracy, stability, and efficiency.