Publications

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

Bibliography:

 K. Bao, Y. Shi, S. Sun, X.-P. Wang, “A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems”, Journal of Computational Physics, 231(24): 8083–8099, 15 October 2012.

Authors:

K. Bao, Y. Shi, S. Sun, X.-P. Wang

Keywords:

Moving contact line; Generalized Navier boundary condition; Finite element method; Convex splitting; Navier–Stokes equations; Cahn–Hilliard equations

Year:

2012

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.

ISSN:

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