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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Vydáno v:	Journal of computational physics Ročník 231; číslo 4; s. 1372 - 1386
Hlavní autoři:	Gao, Min, Wang, Xiao-Ping
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Kidlington Elsevier Inc 20.02.2012 Elsevier
Témata:	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
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Abstract	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.
AbstractList	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. 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 and for the Navier Stokes equations has the better accuracy for pressure. 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.
Author	Gao, Min Wang, Xiao-Ping
Author_xml	– sequence: 1 givenname: Min surname: Gao fullname: Gao, Min email: gaomin@ust.hk – sequence: 2 givenname: Xiao-Ping surname: Wang fullname: Wang, Xiao-Ping email: mawang@ust.hk
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Keywords	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
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Snippet	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...
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SubjectTerms	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
Title	A gradient stable scheme for a phase field model for the moving contact line problem
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