## 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.author He, Qiaolin dc.contributor.author Glowinski, Roland dc.contributor.author Wang, Xiao Ping dc.contributor.institution Department of Mathematics, Sichuan University, Chengdu 610064, China dc.contributor.institution Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong dc.contributor.institution Department of Mathematics, University of Houston, Houston, TX 77204, United States dc.contributor.institution Institute of Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong dc.date.accessioned 2016-02-28T07:59:44Z dc.date.available 2016-02-28T07:59:44Z dc.date.issued 2011-06 dc.description.abstract 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. dc.description.sponsorship 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. dc.identifier.citation 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. dc.identifier.doi 10.1016/j.jcp.2011.03.022 dc.identifier.issn 0021-9991 dc.identifier.journal Journal of Computational Physics dc.identifier.uri http://hdl.handle.net/10754/600238 dc.publisher Elsevier BV dc.subject Cahn-Hilliard dc.subject Conjugate gradient dc.subject Contact line dc.subject Least squares dc.subject Navier-Stokes dc.subject Operator-splitting dc.title 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.type Article display.details.left
Type
Article

Authors
He, Qiaolin
Glowinski, Roland
Wang, Xiao Ping

KAUST Grant Number
SA-C0040
UK-C0016

Date
2011-06
display.details.right
Abstract
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.

Citation
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.

Acknowledgements
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.

Publisher
Elsevier BV

Journal
Journal of Computational Physics

DOI
10.1016/j.jcp.2011.03.022
kaust.grant.fundedcenter KAUST-HKUST Micro/Nanofluidic Joint Laboratory kaust.grant.number SA-C0040 kaust.grant.number UK-C0016 kaust.person Wang, Xiao-Ping orcid.author He, Qiaolin orcid.author Glowinski, Roland orcid.author Wang, Xiao Ping