An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Lingyue Shen; Huaxiong Huang; Ping Lin; Zilong Song; Shixin Xu

doi:10.1016/j.jcp.2019.109179

An energy stable C⁰ finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

Lingyue Shen, Huaxiong Huang, Ping Lin, Zilong Song, Shixin Xu (Lead / Corresponding author)

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C⁰ finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P¹ element and P² element are energy stable.

Original language	English
Article number	109179
Pages (from-to)	1-27
Number of pages	27
Journal	Journal of Computational Physics
Volume	405
Early online date	10 Dec 2019
DOIs	https://doi.org/10.1016/j.jcp.2019.109179
Publication status	Published - 15 Mar 2020

Keywords

C finite element
Energy stability
Large density ratio
Moving contact lines
Phase-field method
Quasi-incompressible

Access to Document

10.1016/j.jcp.2019.109179

Author Accepted ManuscriptAccepted author manuscript, 8.56 MBLicence: CC BY-NC-ND

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Lin, Ping
- p.lin@dundee.ac.uk
- Mathematics - Professor of Numerical Analysis
Person: Academic

Cite this

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title = "An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density",

abstract = "In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.",

keywords = "C finite element, Energy stability, Large density ratio, Moving contact lines, Phase-field method, Quasi-incompressible",

author = "Lingyue Shen and Huaxiong Huang and Ping Lin and Zilong Song and Shixin Xu",

note = "Funding Information: This work was partially supported by the NSFC (grant numbers 11771040 , 11861131004 , 91430106 ), NSERC (CA) and the Fields Institute . Lingyue Shen was partially supported by the Chinese Scholarship Council for studying at the University of Dundee. Appendix A Publisher Copyright: {\textcopyright} 2019 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

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doi = "10.1016/j.jcp.2019.109179",

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An energy stable C⁰ finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density. / Shen, Lingyue; Huang, Huaxiong; Lin, Ping; Song, Zilong; Xu, Shixin (Lead / Corresponding author).

In: Journal of Computational Physics, Vol. 405, 109179, 15.03.2020, p. 1-27.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - An energy stable C0 finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density

AU - Shen, Lingyue

AU - Huang, Huaxiong

AU - Lin, Ping

AU - Song, Zilong

AU - Xu, Shixin

N1 - Funding Information: This work was partially supported by the NSFC (grant numbers 11771040 , 11861131004 , 91430106 ), NSERC (CA) and the Fields Institute . Lingyue Shen was partially supported by the Chinese Scholarship Council for studying at the University of Dundee. Appendix A Publisher Copyright: © 2019 Elsevier Inc. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/3/15

Y1 - 2020/3/15

N2 - In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.

AB - In this paper, we focus on modeling and simulation of two-phase flow problems with moving contact lines and variable density. A thermodynamically consistent phase-field model with general Navier boundary condition is developed based on the concept of quasi-incompressibility and the energy variational method. A mass conserving C0 finite element scheme is proposed to solve the PDE system. Energy stability is achieved at the fully discrete level. Various numerical results confirm that the proposed scheme for both P1 element and P2 element are energy stable.

KW - C finite element

KW - Energy stability

KW - Large density ratio

KW - Moving contact lines

KW - Phase-field method

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