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In this paper we construct new fully decoupled and high-orderimplicit-explicit (IMEX) schemes for the two-phase incompressible flows basedon the new generalized scalar auxiliary variable approach with optimal energyapproximation (EOP-GSAV) for Cahn-Hilliard equation and consistent splittingmethod for Navier-Stokes equation. These schemes are linear, fully decoupled,unconditionally energy stable, only require solving a sequence of ellipticequations with constant coefficients at each time step, and provide a newtechnique to preserve the consistency between original energy and modifiedenergy. We derive that numerical solutions of these schemes are uniformlybounded without any restriction on time step size. Furthermore, we carry out arigorous error analysis for the first-order scheme and establish optimal globalerror estimates for the phase function, velocity and pressure in two andthree-dimensional cases. Numerical examples are presented to validate theproposed schemes.

Global error estimates of high-order fully decoupled schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows