In this paper, we focus on modeling and simulation of two-phase flow 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. Then a mass conserving and energy stable C0 finite element scheme is developed to solve the PDE system. Various numerical simulation results show that the proposed schemes are mass conservative, energy stable and the 2nd order for P1 element and 3rd order for P2 element convergence rate in the sense of L2 norm.
Numerical Approximations for a Phase-Field Moving Contact Line Model with Variable Densities and Viscosities
NCMIS & LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science（计算数学与科学工程计算研究所，中国科学院数学与系统科学研究院）；Department of Mathematics, University of South Carolina（南卡罗来纳大学数学系）
A structure--preserving ALE--BGN--MDR method for Navier--Stokes free boundary problems with moving contact lines and gravity
Universität Regensburg（雷根斯堡大学）；The Hong Kong Polytechnic University（香港理工大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）
Decoupled, Energy Stable Scheme for Hydrodynamic Allen-Cahn Phase Field Moving Contact Line Model
Institute of Applied Physics and Computational Mathematics（应用物理与计算数学研究所）；School of Science, Beijing University of Posts and Telecommunications（北京邮电大学理学院）；Department of Mathematics, University of South Carolina（南卡罗来纳大学数学系）；School of Mathematical Sciences, Beijing Normal University（北京师范大学数学科学学院）；Laboratory of Mathematics and Complex Systems, Ministry of Education（教育部数学与复杂系统重点实验室）
Efficient Second Order Unconditionally Stable Schemes for a Phase-field Moving Contact Line Model Using Invariant Energy Quadratization Approach
University of South Carolina（南卡罗来纳大学）；University of Electronic Science and Technology of China（电子科技大学）；Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science（中国科学院数学与系统科学研究院计算数学与科学工程计算研究所）；University of Chinese Academy of Sciences（中国科学院大学）
