A gradient stable scheme for a phase field model for the moving contact line problem
KAUST Grant NumberSA-C0040/UK-C0016
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AbstractIn 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. © 2011 Elsevier Inc.
CitationGao M, Wang X-P (2012) A gradient stable scheme for a phase field model for the moving contact line problem. Journal of Computational Physics 231: 1372–1386. Available: http://dx.doi.org/10.1016/j.jcp.2011.10.015.
SponsorsThis 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), Hong Kong RGC-GRF Grants 603107, 604209 and the National Basic Research Program Project of China under project 2009CB623200. Min Gao is a Ph.D. student under HKUST-Shanghai Jiaotong University collaboration program.
JournalJournal of Computational Physics