Numerical approximations for a phase-field moving contact line model with variable densities and viscosities

We consider the numerical approximations of a two-phase hydrodynamics coupled phase field model that incorporates the variable densities, viscosities and moving contact line boundary conditions. The model is a nonlinear, coupled system that consists of incompressible Navier-Stokes equations with the generalized Navier boundary condition, and the Cahn-Hilliard equations with moving contact line boundary conditions. By some subtle explicit-implicit treatments to nonlinear terms, we develop two efficient, unconditionally energy stable numerical schemes, in particular, a linear decoupled energy stable scheme for the system with static contact line condition, and a nonlinear energy stable scheme for the system with dynamic contact line condition. An efficient spectralGalerkin spatial discretization is implemented to verify the accuracy and efficiency of proposed schemes. Various numerical results show that the proposed schemes are efficient and accurate. (C) 2017 Elsevier Inc. All rights reserved.