In this article, we propose to study two issues associated with the use of the incremental projection method for solving the incompressible Navier-Stokes equation. The first one is the combination of this time splitting algorithm with an adaptive local refinement method. The second one is the reduction of spurious velocities due to the right-hand side of the momentum balance. We propose a new variant of the incremental projection method for solving the Navier-Stokes equations with variable density and illustrate its behaviour with the example of two phase flows simulations using a Cahn-Hilliard/Navier-Stokes model.