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

Handle URI:
http://hdl.handle.net/10754/562340
Title:
A finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problems
Authors:
Bao, Kai; Shi, Yi; Sun, Shuyu ( 0000-0002-3078-864X ) ; Wang, Xiaoping
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..
KAUST Department:
Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Physical Sciences and Engineering (PSE) Division; Environmental Science and Engineering Program; Computational Transport Phenomena Lab
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
Issue Date:
Oct-2012
DOI:
10.1016/j.jcp.2012.07.027
Type:
Article
ISSN:
00219991
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.
Appears in Collections:
Articles; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Sciences and Engineering (PSE) Division; Computational Transport Phenomena Lab; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorBao, Kaien
dc.contributor.authorShi, Yien
dc.contributor.authorSun, Shuyuen
dc.contributor.authorWang, Xiaopingen
dc.date.accessioned2015-08-03T10:01:34Zen
dc.date.available2015-08-03T10:01:34Zen
dc.date.issued2012-10en
dc.identifier.issn00219991en
dc.identifier.doi10.1016/j.jcp.2012.07.027en
dc.identifier.urihttp://hdl.handle.net/10754/562340en
dc.description.abstractIn 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..en
dc.description.sponsorshipThis 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.en
dc.publisherElsevier BVen
dc.subjectCahn-Hilliard equationsen
dc.subjectConvex splittingen
dc.subjectFinite element methoden
dc.subjectGeneralized Navier boundary conditionen
dc.subjectMoving contact lineen
dc.subjectNavier-Stokes equationsen
dc.titleA finite element method for the numerical solution of the coupled Cahn-Hilliard and Navier-Stokes system for moving contact line problemsen
dc.typeArticleen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Divisionen
dc.contributor.departmentEnvironmental Science and Engineering Programen
dc.contributor.departmentComputational Transport Phenomena Laben
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionDepartment of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, Chinaen
kaust.authorBao, Kaien
kaust.authorSun, Shuyuen
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