  We construct first- and second-order time discretization schemes for the
Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary
variables approach (MSAV) approach for gradient systems and (rotational)
pressure-correction for Navier-Stokes equations. These schemes are linear,
fully decoupled, unconditionally energy stable, and only require solving a
sequence of elliptic equations with constant coefficients at each time step. We
carry out a rigorous error analysis for the first-order scheme, establishing
optimal convergence rate for all relevant functions in different norms. We also
provide numerical experiments to verify our theoretical results.
