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Link to original content: https://doi.org/10.1007/s10915-016-0283-9
Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow | Journal of Scientific Computing Skip to main content
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Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow

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Abstract

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.

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Acknowledgments

H. Li is partially supported by NSFC grant NSFC-11471372. Q. Wang is partially supported by NSF grants DMS-1200487, DMS-1517347, AFOSR Grant FA9550-12-1-0178 and an SC EPSCOR GEAR award. X. Yang is partially supported by NSF Grants DMS-1200487, DMS-1418898, and AFOSR Grant FA9550-12-1-0178. The authors thank Professor Chun Liu for stimulating discussions and insightful comments. X. Yang thanks Institute of Software of Chinese Academy of Science for using their facilities for this research. J. Zhao and X. Yang thank the hospitality of Beijing Computational Science Research Center during their visits when the research was done.

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Authors and Affiliations

  1. Department of Mathematics, University of South Carolina, Columbia, SC, 29208, USA

    Jia Zhao, Qi Wang & Xiaofeng Yang

  2. Chinese Academy of Science, Institute of Software, Beijing, China

    Huiyuan Li

  3. Beijing Computational Science Research Center, Beijing, China

    Qi Wang

  4. School of Mathematics, Nankai University, Tianjin, China

    Qi Wang

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  1. Jia Zhao
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  2. Huiyuan Li
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  4. Xiaofeng Yang
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Correspondence to Xiaofeng Yang.

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Zhao, J., Li, H., Wang, Q. et al. Decoupled Energy Stable Schemes for a Phase Field Model of Three-Phase Incompressible Viscous Fluid Flow. J Sci Comput 70, 1367–1389 (2017). https://doi.org/10.1007/s10915-016-0283-9

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