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

Kai Bao, Yi Shi, Shuyu Sun, Xiaoping Wang

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48 Scopus citations

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. © 2012 Elsevier Inc..
Original languageEnglish (US)
Pages (from-to)8083-8099
Number of pages17
JournalJournal of Computational Physics
Volume231
Issue number24
DOIs
StatePublished - Oct 2012

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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