Hele-Shaw槽内Cahn-Hilliard二元表面活性剂模型的全离散、解耦、二阶时准和能量稳定有限元格式

IF 1.9 3区 数学 Q2 Mathematics
Xiaofeng Yang
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引用次数: 4

摘要

考虑了Hele-Shaw槽内二元流体表面活性剂相场模型的数值近似,该模型包含两个耦合的Cahn-Hilliard方程和Darcy方程。我们开发了一个完全离散的有限元格式,具有一些期望的特性,包括线性,二阶时间精度,解耦结构和无条件能量稳定性。该方案结合了Darcy方程的投影法、非线性能量势的二次化方法和基于“{零能量贡献}”特征的平凡ODE的解耦方法。该方案的优点是,不仅可以解耦计算所有变量,而且每个方程在每个时间步长只有常系数。严格证明了该方案满足无条件能量稳定,并给出了详细的实现过程。为了验证该方案的有效性,文中还对不同流型下的基准Saffman-Taylor指指不稳定性问题进行了数值模拟,验证了表面活性剂对表面张力的减弱作用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme  of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell
We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the ``{zero-energy-contribution}" feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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