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