An augmented method for free boundary problems with moving contact lines

Zhilin Li*, Ming-Chih Lai, Guowei He, Hongkai Zhao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


An augmented immersed interface method (IIM) is proposed for simulating one-phase moving contact line problems in which a liquid drop spreads or recoils on a solid substrate. While the present two-dimensional mathematical model is a free boundary problem, in our new numerical method, the fluid domain enclosed by the free boundary is embedded into a rectangular one so that the problem can be solved by a regular Cartesian grid method. We introduce an augmented variable along the free boundary so that the stress balancing boundary condition is satisfied. A hybrid time discretization is used in the projection method for better stability. The resultant Helmholtz/Poisson equations with interfaces then are solved by the IIM in an efficient way. Several numerical tests including an accuracy check, and the spreading and recoiling processes of a liquid drop are presented in detail.

Original languageEnglish
Pages (from-to)1033-1040
Number of pages8
JournalComputers and Fluids
Issue number6
StatePublished - 1 Jun 2010


  • Augmented method
  • Embedding technique
  • Free boundary problem
  • Immersed interface method
  • Irregular domain
  • Moving contact line
  • Navier-Stokes equations
  • One-phase flow
  • Triple junction

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