In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation (EOP-GSAV) for Cahn-Hilliard equation and consistent splitting method for Navier-Stokes equation. These schemes are linear, fully decoupled, unconditionally energy stable, only require solving a sequence of elliptic equations with constant coefficients at each time step, and provide a new technique to preserve the consistency between original energy and modified energy. We derive that numerical solutions of these schemes are uniformly bounded without any restriction on time step size. Furthermore, we carry out a rigorous error analysis for the first-order scheme and establish optimal global error estimates for the phase function, velocity and pressure in two and three-dimensional cases. Numerical examples are presented to validate the proposed schemes.

翻译：本文基于针对Cahn-Hilliard方程提出的具有最优能量逼近的新型广义标量辅助变量法（EOP-GSAV）以及Navier-Stokes方程的一致分裂方法，构建了用于两相不可压缩流的新型全解耦高阶隐式-显式（IMEX）格式。这些格式具有线性、完全解耦、无条件能量稳定的特性，每个时间步仅需求解一系列常系数椭圆方程，并提供了一种保持原始能量与修正能量一致性的新技术。我们推导了这些格式的数值解在时间步长无任何限制条件下的一致有界性。此外，我们对一阶格式进行了严格的误差分析，并在二维和三维情形下建立了相函数、速度和压力的最优全局误差估计。数值算例验证了所提格式的有效性。