  A novel numerical scheme including time and spatial discretization is offered
for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this
paper. Variable densities and viscosities are considered in the nu-merical
scheme. By introducing an intermediate velocity in both Cahn-Hilliard equation
and momentum equation, the scheme can keep discrete energy law. A decouple
approach based on pressure stabilization is implemented to solve the
Navier-Stokes part, while the stabilization or convex splitting method is
adopt-ed for the Cahn-Hilliard part. This novel scheme is totally decoupled,
linear, unconditionally energy stable for incompressible two-phase flow diffuse
inter-face model. Numerical results demonstrate the validation, accuracy,
robustness and discrete energy law of the proposed scheme in this paper.
