  We construct a numerical scheme based on the scalar auxiliary variable (SAV)
approach in time and the MAC discretization in space for the
Cahn-Hilliard-Navier-Stokes phase field model, and carry out stability and
error analysis. The scheme is linear, second-order, unconditionally energy
stable and can be implemented very efficiently. We establish second-order error
estimates both in time and space for phase field variable, chemical potential,
velocity and pressure in different discrete norms. We also provide numerical
experiments to verify our theoretical results and demonstrate the robustness
and accuracy of the our scheme.
