Journal of Scientific Computing

, Volume 72, Issue 3, pp 1119–1145 | Cite as

A Parallel Finite Element Method for 3D Two-Phase Moving Contact Line Problems in Complex Domains

  • Li Luo
  • Qian Zhang
  • Xiao-Ping WangEmail author
  • Xiao-Chuan Cai


Moving contact line problem plays an important role in fluid-fluid interface motion on solid surfaces. The problem can be described by a phase-field model consisting of the coupled Cahn–Hilliard and Navier–Stokes equations with the generalized Navier boundary condition (GNBC). Accurate simulation of the interface and contact line motion requires very fine meshes, and the computation in 3D is even more challenging. Thus, the use of high performance computers and scalable parallel algorithms are indispensable. In this paper, we generalize the GNBC to surfaces with complex geometry and introduce a finite element method on unstructured 3D meshes with a semi-implicit time integration scheme. A highly parallel solution strategy using different solvers for different components of the discretization is presented. More precisely, we apply a restricted additive Schwarz preconditioned GMRES method to solve the systems arising from implicit discretization of the Cahn–Hilliard equation and the velocity equation, and an algebraic multigrid preconditioned CG method to solve the pressure Poisson system. Numerical experiments show that the strategy is efficient and scalable for 3D problems with complex geometry and on a supercomputer with a large number of processors.


Two-phase flows Moving contact line Phase-field model Unstructured mesh Finite element method Scalable parallel algorithms 



This publication was supported in part by the Hong Kong RGC-GRF grants 605513, 16302715, RGC-CRF grant C6004-14G, NSFC-REGC joint research scheme N-HKUST620/15 and the Chinese National 863 Plan Program 2015AA01A302.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Li Luo
    • 1
  • Qian Zhang
    • 1
  • Xiao-Ping Wang
    • 1
    Email author
  • Xiao-Chuan Cai
    • 2
  1. 1.Department of MathematicsThe Hong Kong University of Science and Technology, Clear Water BayKowloonHong Kong
  2. 2.Department of Computer ScienceUniversity of Colorado BoulderBoulderUSA

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