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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65 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

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): SA-C0040/UK-C0016
Acknowledgements: This publication was based on work supported in part by Award No. SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST), the Hong Kong RGC-GRF Grants 605311 and 604209 and the national basic research program under project of China under project 2009CB623200. The work is also supported by the project entitled "The Modeling and Simulation of Two-Phase Flow in Porous Media: From Pore Scale to Darcy Scale" funded by KAUST's GRP-CF (Global Research Partnership Collaborative Fellows) Program.

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)
  • Computer Science Applications

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