Thermodynamically consistent hydrodynamic phase-field computational modeling for fluid-structure interaction with moving contact lines
Thermodynamically consistent hydrodynamic phase-field computational modeling for fluid-structure interaction with moving contact lines
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DOI：
10.1016/j.jcp.2023.112409
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发表时间：
2023-08
期刊：
影响因子：
--
通讯作者：
Qi Hong;Yuezheng Gong;Jia Zhao
中科院分区：
文献类型：
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作者：
Qi Hong;Yuezheng Gong;Jia Zhao
本文提出了一种新颖的计算建模方法来研究与移动接触线的流固相互作用。通过采用广义 Onsager 原理，引入了耦合流体动力学和相场系统，该系统可以以热力学一致的方式描述与移动接触线的流体-结构相互作用。所得偏微分方程 (PDE) 模型由纳维-斯托克斯方程和非线性 Allen-Cahn 型方程组成。体积守恒是通过附加惩罚项来强制执行的。结合多种技术，提出了一种全离散保结构数值方案，以有效、准确地求解该耦合偏微分方程组。对于时间离散化，我们利用补充变量方法来保留热力学结构，并利用投影方法来减小问题规模。然后，我们在交错网格上使用有限差分方法进行空间离散。此外，我们还严格证明了所提出的基于二阶后向差分公式的数值格式尊重原始能量稳定性，即该格式是能量稳定的。此外，借助补充变量方法，所得方案可以转化为约束优化问题，其中补充变量的解是达到最优的目标函数的参数。然后部分引入增强拉格朗日方法，以提高解决此类约束优化问题的鲁棒性和效率。最后，各种数值模拟验证了模型的能力并证明了方案的有效性、准确性和稳定性。
This paper proposes a novel computational modeling approach to investigate the fluid-structure interactions with moving contact lines. By embracing the generalized Onsager principle, a coupled hydrodynamics and phase field system is introduced that can describe the fluid-structure interactions with moving contact lines in a thermodynamically consistent manner. The resulting partial differential equation (PDE) model consists of the Navier-Stokes equation and a nonlinear Allen-Cahn type equation. Volume conservation is enforced through an additional penalty term. A fully-discrete structure-preserving numerical scheme is proposed by combining several techniques to solve this coupled PDE system effectively and accurately. For the temporal discretization, we utilize the supplementary variable method for preserving the thermodynamic structure and the projection approach for reducing the problem size. Then, we use the finite difference method on the staggered grid for spatial discretization. Furthermore, we have rigorously proved that the proposed numerical scheme based on the second-order backward difference formula respects the original energy stability, i.e., the scheme is energy stable. Additionally, with the aid of the supplementary variable method, the resultant scheme can be transformed into a constrained optimization problem, where the solutions of the supplementary variables are the arguments of the objective function that reaches the optimality. Then the augmented Lagrangian method is introduced in part to bring robustness and efficiency to solving such a constrained optimization problem. Finally, various numerical simulations verify the model's capability and demonstrate the scheme's effectiveness, accuracy, and stability.