Numerical analysis of a continuum model of phase transition
SIAM Journal on Numerical Analysis
Accurate projection methods for the incompressible Navier—Stokes equations
Journal of Computational Physics
A new class of truly consistent splitting schemes for incompressible flows
Journal of Computational Physics
Conservative multigrid methods for Cahn-Hilliard fluids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Diffuse interface model for incompressible two-phase flows with large density ratios
Journal of Computational Physics
An efficient moving mesh spectral method for the phase-field model of two-phase flows
Journal of Computational Physics
Journal of Computational Physics
An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
In this paper, an efficient numerical scheme is designed for a phase field model for the moving contact line problem, which consists of a coupled system of the Cahn-Hilliard and Navier-Stokes equations with the generalized Navier boundary condition [1,2,4]. The nonlinear version of the scheme is semi-implicit in time and is based on a convex splitting of the Cahn-Hilliard free energy (including the boundary energy) together with a projection method for the Navier-Stokes equations. We show, under certain conditions, the scheme has the total energy decaying property and is unconditionally stable. The linearized scheme is easy to implement and introduces only mild CFL time constraint. Numerical tests are carried out to verify the accuracy and stability of the scheme. The behavior of the solution near the contact line is examined. It is verified that, when the interface intersects with the boundary, the consistent splitting scheme [21,22] for the Navier Stokes equations has the better accuracy for pressure.