论文标题
在完全脱钩的MSAV方案上
On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows
论文作者
论文摘要
我们基于梯度系统的多个标量辅助变量方法（MSAV）方法，为Cahn-Hilliard-Navier-Stokes系统构建一阶和二阶时间离散方案，用于梯度系统和Navier-Stokes方程的（旋转）压力纠正。这些方案是线性的，完全脱钩的，无条件的能量稳定，并且只需要在每个时间步骤求解具有恒定系数的椭圆方程序列。我们对一阶方案进行了严格的错误分析，为不同规范中所有相关功能建立了最佳收敛率。我们还提供数值实验来验证我们的理论结果。
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.
