A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems

  • Authors:

  • Kai Bao;Yi Shi;Shuyu Sun;Xiao-Ping Wang

  • Affiliations:

  • Division of Mathematics and Computer Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia and Department of Mathematics, The Hong Kong Unive ...;Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China;Division of Mathematics and Computer Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia;Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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Abstract

In this paper, a semi-implicit finite element method is presented for the coupled Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition for the moving contact line problems. In our method, the system is solved in a decoupled way. For the Cahn-Hilliard equations, a convex splitting scheme is used along with a P1-P1 finite element discretization. The scheme is unconditionally stable. A linearized semi-implicit P2-P0 mixed finite element method is employed to solve the Navier-Stokes equations. With our method, the generalized Navier boundary condition is extended to handle the moving contact line problems with complex boundary in a very natural way. The efficiency and capacity of the present method are well demonstrated with several numerical examples.