A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line

dc.contributor.authorHe, Qiaolin
dc.contributor.authorGlowinski, Roland
dc.contributor.authorWang, Xiao Ping
dc.contributor.institutionDepartment of Mathematics, Sichuan University, Chengdu 610064, China
dc.contributor.institutionDepartment of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
dc.contributor.institutionDepartment of Mathematics, University of Houston, Houston, TX 77204, United States
dc.contributor.institutionInstitute of Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
dc.date.accessioned2016-02-28T07:59:44Z
dc.date.available2016-02-28T07:59:44Z
dc.date.issued2011-06
dc.description.abstractIn this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.
dc.description.sponsorshipQL He and XP Wang are supported in part by Hong Kong RGC-CERG Grants 603107 and 604209. QL He is supported in part by Youth Foundation of Sichuan University No 2010SCU11072. XPW is also supported in part by Award No SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST). R. Glowinski acknowledges the support of the Institute for Advanced Study (IAS) at The Hong Kong University of Science and Technology.
dc.identifier.citationHe Q, Glowinski R, Wang X-P (2011) A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line. Journal of Computational Physics 230: 4991–5009. Available: http://dx.doi.org/10.1016/j.jcp.2011.03.022.
dc.identifier.doi10.1016/j.jcp.2011.03.022
dc.identifier.issn0021-9991
dc.identifier.journalJournal of Computational Physics
dc.identifier.urihttp://hdl.handle.net/10754/600238
dc.publisherElsevier BV
dc.subjectCahn-Hilliard
dc.subjectConjugate gradient
dc.subjectContact line
dc.subjectLeast squares
dc.subjectNavier-Stokes
dc.subjectOperator-splitting
dc.titleA least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line
dc.typeArticle
display.details.left<span><h5>Type</h5>Article<br><br><h5>Authors</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=He, Qiaolin,equals">He, Qiaolin</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Glowinski, Roland,equals">Glowinski, Roland</a><br><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.author=Wang, Xiao Ping,equals">Wang, Xiao Ping</a><br><br><h5>KAUST Grant Number</h5>SA-C0040<br>UK-C0016<br><br><h5>Date</h5>2011-06</span>
display.details.right<span><h5>Abstract</h5>In this article we discuss the numerical solution of the Navier-Stokes-Cahn-Hilliard system modeling the motion of the contact line separating two immiscible incompressible viscous fluids near a solid wall. The method we employ combines a finite element space approximation with a time discretization by operator-splitting. To solve the Cahn-Hilliard part of the problem, we use a least-squares/conjugate gradient method. We also show that the scheme has the total energy decaying in time property under certain conditions. Our numerical experiments indicate that the method discussed here is accurate, stable and efficient. © 2011 Elsevier Inc.<br><br><h5>Citation</h5>He Q, Glowinski R, Wang X-P (2011) A least-squares/finite element method for the numerical solution of the Navier–Stokes-Cahn–Hilliard system modeling the motion of the contact line. Journal of Computational Physics 230: 4991–5009. Available: http://dx.doi.org/10.1016/j.jcp.2011.03.022.<br><br><h5>Acknowledgements</h5>QL He and XP Wang are supported in part by Hong Kong RGC-CERG Grants 603107 and 604209. QL He is supported in part by Youth Foundation of Sichuan University No 2010SCU11072. XPW is also supported in part by Award No SA-C0040/UK-C0016, made by King Abdullah University of Science and Technology (KAUST). R. Glowinski acknowledges the support of the Institute for Advanced Study (IAS) at The Hong Kong University of Science and Technology.<br><br><h5>Publisher</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.publisher=Elsevier BV,equals">Elsevier BV</a><br><br><h5>Journal</h5><a href="https://repository.kaust.edu.sa/search?spc.sf=dc.date.issued&spc.sd=DESC&f.journal=Journal of Computational Physics,equals">Journal of Computational Physics</a><br><br><h5>DOI</h5><a href="https://doi.org/10.1016/j.jcp.2011.03.022">10.1016/j.jcp.2011.03.022</a></span>
kaust.grant.fundedcenterKAUST-HKUST Micro/Nanofluidic Joint Laboratory
kaust.grant.numberSA-C0040
kaust.grant.numberUK-C0016
kaust.personWang, Xiao-Ping
orcid.authorHe, Qiaolin
orcid.authorGlowinski, Roland
orcid.authorWang, Xiao Ping
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