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

Citation data:

Journal of Computational Physics, ISSN: 0021-9991, Vol: 231, Issue: 24, Page: 8083-8099

Publication Year:
2012
Usage 55
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Captures 42
Readers 42
Citations 28
Citation Indexes 28
Repository URL:
http://hdl.handle.net/10754/562340
DOI:
10.1016/j.jcp.2012.07.027
Author(s):
Bao, Kai; Shi, Yi; Sun, Shuyu; Wang, Xiaoping
Publisher(s):
Elsevier BV; Elsevier
Tags:
Physics and Astronomy; Computer Science; Cahn-Hilliard equations; Convex splitting; Finite element method; Generalized Navier boundary condition; Moving contact line; Navier-Stokes equations
article description
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.