  In this paper, we present an efficient energy stable scheme to solve a phase
field model incorporating contact line condition. Instead of the usually used
Cahn-Hilliard type phase equation, we adopt the Allen-Cahn type phase field
model with the static contact line boundary condition that coupled with
incompressible Navier-Stokes equations with Navier boundary condition. The
projection method is used to deal with the Navier-Stokes equa- tions and an
auxiliary function is introduced for the non-convex Ginzburg-Landau bulk
potential. We show that the scheme is linear, decoupled and energy stable.
Moreover, we prove that fully discrete scheme is also energy stable. An
efficient finite element spatial discretization method is implemented to verify
the accuracy and efficiency of proposed schemes. Numerical results show that
the proposed scheme is very efficient and accurate
