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

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    Type
    Article
    Authors
    Bao, Kai
    Shi, Yi
    Sun, Shuyu cc
    Wang, Xiaoping
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computational Transport Phenomena Lab
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    KAUST Grant Number
    SA-C0040/UK-C0016
    Date
    2012-10
    Permanent link to this record
    http://hdl.handle.net/10754/562340
    
    Metadata
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    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. © 2012 Elsevier Inc..
    Citation
    Bao, K., Shi, Y., Sun, S., & Wang, X.-P. (2012). 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. doi:10.1016/j.jcp.2012.07.027
    Sponsors
    This 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), the Hong Kong RGC-GRF Grants 605311 and 604209 and the national basic research program under project of China under project 2009CB623200. The work is also supported by the project entitled "The Modeling and Simulation of Two-Phase Flow in Porous Media: From Pore Scale to Darcy Scale" funded by KAUST's GRP-CF (Global Research Partnership Collaborative Fellows) Program.
    Publisher
    Elsevier BV
    Journal
    Journal of Computational Physics
    DOI
    10.1016/j.jcp.2012.07.027
    ae974a485f413a2113503eed53cd6c53
    10.1016/j.jcp.2012.07.027
    Scopus Count
    Collections
    Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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