We construct first- and second-order time discretization schemes for the Cahn–Hilliard–Navier–Stokes system based on the multiple scalar auxiliary variables (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.

中文翻译：

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关于两相不可压缩流动的 Cahn-Hilliard-Navier-Stokes 模型的完全解耦 MSAV 方案

我们基于梯度系统的多标量辅助变量 (MSAV) 方法和 Navier-Stokes 方程的（旋转）压力校正，构建了 Cahn-Hilliard-Navier-Stokes 系统的一阶和二阶时间离散化方案。这些方案是线性的、完全解耦的、无条件能量稳定的，并且只需要在每个时间步求解一系列具有常系数的椭圆方程。我们对一阶方案进行了严格的误差分析，为不同范数下的所有相关函数建立了最佳收敛速度。我们还提供数值实验来验证我们的理论结果。