Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow
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- 作者：Jia Zhao ; Huiyuan Li ; Qi Wang ; Xiaofeng Yang
- 关键词：Phase ; field ; Multiphase flows ; Navier–Stokes ; Allen–Cahn ; Cahn–Hilliard ; Stability
- 刊名：Journal of Scientific Computing
- 出版年：2017
- 出版时间：March 2017
- 年：2017
- 卷：70
- 期：3
- 页码：1367-1389
- 全文大小：
- 刊物类别：Mathematics and Statistics
- 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
- 出版者：Springer US
- ISSN：1573-7691
- 卷排序：70
文摘
We develop a numerical approximation for a hydrodynamic phase field model of three immiscible, incompressible viscous fluid phases. The model is derived from a generalized Onsager principle following an energetic variational formulation and is consisted of the momentum transport equation and coupled phase transport equations. It conserves the volume of each phase and warrants the total energy dissipation in time. Its numerical approximation is given by a set of easy-to-implement, semi-discrete, linear, decoupled elliptic equations at each time step, which can be solved efficiently using fast solvers. We prove that the scheme is energy stable. Mesh refinement tests and three numerical examples of three-phase viscous fluid flows in 3D are presented to benchmark the effectiveness of the model as well as the efficiency of the numerical scheme.