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)

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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 languageEnglish
Article number109179
Pages (from-to)1-27
Number of pages27
JournalJournal of Computational Physics
Early online date10 Dec 2019
Publication statusPublished - 15 Mar 2020



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

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