Efficient Fully decoupled and second-order time-accurate scheme for the Navier-Stokes coupled Cahn-Hilliard Ohta-Kawaski Phase-Field model of Diblock copolymer melt
Efficient Fully decoupled and second-order time-accurate scheme for the Navier-Stokes coupled Cahn-Hilliard Ohta-Kawaski Phase-Field model of Diblock copolymer melt
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DOI：
10.1016/j.cam.2021.113843
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Tongmao Li;Peng Liu;Jun Zhang;Xiaofeng Yang
中科院分区：
文献类型：
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作者：
Tongmao Li;Peng Liu;Jun Zhang;Xiaofeng Yang
在这项工作中，我们旨在为两嵌段共聚物熔体的流动耦合相场模型开发一种高效的数值格式。形式上，该模型是一个非常复杂的非线性系统，由具有Ohta-Kawaski势的Navier-Stokes方程和Cahn-Hilliard类型的方程组成。通过一种新的解耦技术和投影法的结合，我们建立了该模型的第一个完全解耦、能量稳定、二阶时间精度的数值格式。解耦技术基于辅助微分器的设计，辅助微分器在获得完全解耦结构的同时保持能量稳定起着至关重要的作用。该格式的高效率不仅体现在它的线性和解耦结构上，而且还因为它在每个时间步只需要求解几个椭圆型方程。我们严格证明了该方案满足无条件能量稳定性，并给出了详细的实现过程。数值实验进一步验证了该算法的收敛速度、能量稳定性和有效性。
In this work, we aim to develop a highly efficient numerical scheme for the flow-coupled phase-field model of diblock copolymer melt. Formally, the model is a very complicated nonlinear system that consists of the Navier–Stokes equations and the Cahn–Hilliard type equations with the Ohta–Kawaski potential. Through a combination of a novel decoupling technique and the projection method, we develop the first full decoupling, energy stable, and second-order time-accurate numerical scheme for this model. The decoupling technique is based on the design of an auxiliary ODE, which plays a vital role in obtaining the full decoupling structure while maintaining energy stability. The high efficiency of the scheme is not only reflected by its linear and decoupled structure but also because it only needs to solve a few elliptic equations at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Numerical experiments further verify the convergence rate, energy stability, and effectiveness of the developed algorithm.