A gradient stable scheme for a phase field model for the moving contact line problem

In this paper, an efficient numerical scheme is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn–Hilliard and Navier–Stokes equations with the generalized Navier boundary condition [1,2,4]. The nonlinear version of the scheme is sem...

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Bibliographic Details
Published in:Journal of computational physics Vol. 231; no. 4; pp. 1372 - 1386
Main Authors: Gao, Min, Wang, Xiao-Ping
Format: Journal Article
Language:English
Published: Kidlington Elsevier Inc 20.02.2012
Elsevier
Subjects:
Accuracy
Boundaries
Cahn–Hilliard equation
Computational techniques
Contact
Convex splitting
Exact sciences and technology
Free energy
Mathematical analysis
Mathematical methods in physics
Mathematical models
Moving contact line
Navier-Stokes equations
Phase field
Physics
Splitting
Navier–Stokes equations
Moving contact line
Convex splitting
Cahn–Hilliard equation
Phase field
Cahn-Hilliard equation
Total energy
Cahn Hilliard equation
Boundary conditions
Models
Calculation
Free energy
Navier-Stokes equations
Calculation methods
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:In this paper, an efficient numerical scheme is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn–Hilliard and Navier–Stokes equations with the generalized Navier boundary condition [1,2,4]. The nonlinear version of the scheme is semi-implicit in time and is based on a convex splitting of the Cahn–Hilliard free energy (including the boundary energy) together with a projection method for the Navier–Stokes equations. We show, under certain conditions, the scheme has the total energy decaying property and is unconditionally stable. The linearized scheme is easy to implement and introduces only mild CFL time constraint. Numerical tests are carried out to verify the accuracy and stability of the scheme. The behavior of the solution near the contact line is examined. It is verified that, when the interface intersects with the boundary, the consistent splitting scheme [21,22] for the Navier Stokes equations has the better accuracy for pressure.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2011.10.015