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

被引：11

作者：

Shen, Lingyue ^{[1
]}

Huang, Huaxiong ^{[3
,4
,5
,6
]}

Lin, Ping ^{[1
]}

Song, Zilong ^{[5
,7
]}

Xu, Shixin ^{[2
,6
]}

机构：

[1] Univ Dundee, Dept Math, Dundee DD1 4HN, Scotland

[2] Duke Kunshan Univ, 8 Duke Ave, Kunshan, Jiangsu, Peoples R China

[3] Beijing Normal Univ, Joint Math Res Ctr, Zhuhai, Peoples R China

[4] BNU HKBU United Int Coll, Zhuhai, Peoples R China

[5] York Univ, Dept Math & Stat, Toronto, ON, Canada

[6] Fields Inst Res Math Sci, Ctr Quantitat Anal & Modelling, Toronto, ON, Canada

[7] Univ Calif Riverside, Dept Math, 900 Univ Ave, Riverside, CA 92521 USA

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2020年 / 405卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Energy stability; Moving contact lines; Large density ratio; Phase-field method; Quasi-incompressible; C(0 )finite element; LATTICE BOLTZMANN MODEL; CAHN-HILLIARD; 2-PHASE FLOWS; NUMERICAL APPROXIMATIONS; VARIATIONAL APPROACH; MOLECULAR-DYNAMICS; DIFFERENCE SCHEME; COMPLEX FLUIDS; 2ND-ORDER; INTERFACE;

D O I：

10.1016/j.jcp.2019.109179

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

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 C-0 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 P-1 element and P-2 element are energy stable. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：27

共 30 条

[1] AN ENERGY STABLE C0 FINITE ELEMENT SCHEME FOR A PHASE-FIELD MODEL OF VESICLE MOTION AND DEFORMATION
Shen, Lingyue
Xu, Zhiliang
Lin, Ping
Huang, Huaxiong
Xu, Shixin
SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2022, 44 (01): : B122 - B145
[2] An efficient and energy stable scheme for a phase-field model for the moving contact line problem
Aland, Sebastian
Chen, Feng
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 2016, 81 (11) : 657 - 671
[3] Fully discrete energy stable scheme for a phase-field moving contact line model with variable densities and viscosities
Zhu, Guangpu
Chen, Huangxin
Li, Aifen
Sun, Shuyu
Yao, Jun
APPLIED MATHEMATICAL MODELLING, 2020, 83 : 614 - 639
[4] An energy stable algorithm for a quasi-incompressible hydrodynamic phase-field model of viscous fluid mixtures with variable densities and viscosities
Gong, Yuezheng
Zhao, Jia
Wang, Qi
COMPUTER PHYSICS COMMUNICATIONS, 2017, 219 : 20 - 34
[5] Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density
Liu, Chun
Shen, Jie
Yang, Xiaofeng
JOURNAL OF SCIENTIFIC COMPUTING, 2015, 62 (02) : 601 - 622
[6] Decoupled Energy Stable Schemes for a Phase-Field Model of Two-Phase Incompressible Flows with Variable Density
Chun Liu
Jie Shen
Xiaofeng Yang
Journal of Scientific Computing, 2015, 62 : 601 - 622
[7] An efficient scheme for a phase field model for the moving contact line problem with variable density and viscosity
Gao, Min
Wang, Xiao-Ping
JOURNAL OF COMPUTATIONAL PHYSICS, 2014, 272 : 704 - 718
[8] A gradient stable scheme for a phase field model for the moving contact line problem
Gao, Min
Wang, Xiao-Ping
JOURNAL OF COMPUTATIONAL PHYSICS, 2012, 231 (04) : 1372 - 1386
[9] Numerical approximations for a phase-field moving contact line model with variable densities and viscosities
Yu, Haijun
Yang, Xiaofeng
JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 334 : 665 - 686
[10] A linear second-order in time unconditionally energy stable finite element scheme for a Cahn-Hilliard phase-field model for two-phase incompressible flow of variable densities
Fu, Guosheng
Han, Daozhi
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2021, 387

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