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

Authors:
Qiaolin He;Roland Glowinski;Xiao-Ping Wang
Affiliations:
Department of Mathematics, Sichuan University, Chengdu 610064, PR China and Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Mathematics, University of Houston, Houston, TX 77204, USA and Institute of Advanced Study, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong;Department of Mathematics and KAUST-HKUST Micro/Nanofludic Joint Laboratory, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Venue:
Journal of Computational Physics
Year:
2011

Citing 9
Cited 4

Numerical analysis of a continuum model of phase transition

SIAM Journal on Numerical Analysis
Finite difference schemes for 6u6t= 66x adGdu that inherit energy conservation or dissipation property

Journal of Computational Physics
Wall-driven incompressible viscous flow in a two-dimensional semi-circular cavity

Journal of Computational Physics
Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method

Journal of Computational Physics
On large time-stepping methods for the Cahn--Hilliard equation

Applied Numerical Mathematics
Precursor simulations in spreading using a multi-mesh adaptive finite element method

Journal of Computational Physics
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation

Journal of Computational Physics
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation

SIAM Journal on Numerical Analysis
A Phase-Field Model and Its Numerical Approximation for Two-Phase Incompressible Flows with Different Densities and Viscosities

SIAM Journal on Scientific Computing

A gradient stable scheme for a phase field model for the moving contact line problem

Journal of Computational Physics
A time-stepping scheme involving constant coefficient matrices for phase-field simulations of two-phase incompressible flows with large density ratios

Journal of Computational Physics
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
Numerical methods for a class of nonlinear integro-differential equations

Calcolo: a quarterly on numerical analysis and theory of computation

Quantified Score

Hi-index	31.46

Visualization

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.