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Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density

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Abstract

We consider in this paper numerical approximations of two-phase incompressible flows with different densities and viscosities. We present a variational derivation for a thermodynamically consistent phase-field model that admits an energy law. Two decoupled time discretization schemes for the coupled nonlinear phase-field model are constructed and shown to be energy stable. Numerical experiments are carried out to validate the model and the schemes for problems with large density and viscosity ratios.

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Notes

  1. After we derived the model independently, we learned that the identical model was already derived in [2].

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Acknowledgments

The research of C. Liu is partially supported by NSF DMS-1109107 and DMS-1216938. The research of J. Shen is partially supported in part by NSF DMS-1217066 and AFOSR FA9550-11-1-0328. The work of X. Yang is partially supported by SC EPSCOR GEAR program, AFOSR FA9550-12-1-0178 and NSF DMS-1200487.

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Authors and Affiliations

  1. Department of Mathematics, Penn State University, University Park, PA , 16802, USA

    Chun Liu

  2. Department of Mathematics, Purdue University, West Lafayette, IN , 47907, USA

    Jie Shen

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

    Xiaofeng Yang

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  1. Chun Liu
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  2. Jie Shen
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Correspondence to Jie Shen.

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Liu, C., Shen, J. & Yang, X. Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density. J Sci Comput 62, 601–622 (2015). https://doi.org/10.1007/s10915-014-9867-4

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  • DOI: https://doi.org/10.1007/s10915-014-9867-4

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