Conservative multigrid methods for Cahn-Hilliard fluids
Conservative multigrid methods for Cahn-Hilliard fluids
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DOI：
10.1016/j.jcp.2003.07.035
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发表时间：
2004-01-20
影响因子：
4.1
通讯作者：
Lowengrub, J
中科院分区：
文献类型：
--
作者：
Kim, J;Kang, KK;Lowengrub, J
我们开发了具有相关离散能量泛函的Navier-Stokes （NS）和Cahn-Hilliard （CH）系统的保守的二阶精确全隐式离散化。该系统提供了具有可压缩或不可压缩流动分量的二元流体流动的扩散界面描述[R]。Soc。Lond。Proc,爵士。一个数学。理论物理。Eng。科学通报，2004(5):357 - 357。在这项工作中，我们的重点是流动的情况下包含两个不混相，不可压缩和密度匹配的组件。然而，该方案可以直接扩展到多组件系统。为了在隐式时间水平上有效地求解离散系统，我们开发了一种非线性多网格方法来求解CH方程，然后将其耦合到用于求解NS方程的投影方法中。在有流动和没有流动的情况下，我们用数值方法证明了该方案的收敛性，并通过旋量分解进行了相分离的模拟。我们考察了表面张力和外部流动对分解的单独影响。我们发现表面张力驱动的流动通过界面的收缩增加了聚并率。当施加外部剪切作用时，流动的演变是不平凡的，流动形态随着时间的推移而重复发生多次针尖截断和重连事件。最终，周期运动停止，系统松弛到全局平衡。我们观察到的平衡似乎在所有情况下都具有相似的结构，尽管进化的动力大不相同。我们认为，本文中提出的工作是对具有表面张力的液-液界面进行详细研究的准备，其中界面分离了两种不混溶的流体[关于具有表面张力的液-液射流的pinchoff， in preparation]。为此，我们还包括了有限雷诺数下瑞利不稳定性下液体螺纹的针尖关的模拟。(C) 2003 Elsevier B.V.版权所有
We develop a conservative, second-order accurate fully implicit discretization of the Navier-Stokes (NS) and Cahn-Hilliard (CH) system that has an associated discrete energy functional. This system provides a diffuse-interface description of binary fluid flows with compressible or incompressible flow components [R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998) 2617]. In this work, we focus on the case of flows containing two immiscible, incompressible and density-matched components. The scheme, however, has a straightforward extension to multi-component systems. To efficiently solve the discrete system at the implicit time-level, we develop a nonlinear multigrid method to solve the CH equation which is then coupled to a projection method that is used to solve the NS equation. We demonstrate convergence of our scheme numerically in both the presence and absence of flow and perform simulations of phase separation via spinodal decomposition. We examine the separate effects of surface tension and external flow on the decomposition. We find surface tension driven flow alone increases coalescence rates through the retraction of interfaces. When there is an applied external shear, the evolution of the flow is nontrivial and the flow morphology repeats itself in time as multiple pinchoff and reconnection events occur. Eventually, the periodic motion ceases and the system relaxes to a global equilibrium. The equilibria we observe appears has a similar structure in all cases although the dynamics of the evolution is quite different. We view the work presented in this paper as preparatory for a detailed investigation of liquid-liquid interfaces with surface tension where the interfaces separate two immiscible fluids [On the pinchoff of liquid-liquid jets with surface tension, in preparation]. To this end, we also include a simulation of the pinchoff of a liquid thread under the Rayleigh instability at finite Reynolds number. (C) 2003 Elsevier B.V. All rights reserved.