In this article, based on the grad-div stabilization, we propose a generalized scalar auxiliary variable approach for solving a fluid–fluid interaction problem governed by the Navier–Stokes-ω/Navier–Stokes-ω equations. We adopt the backward Euler scheme and mixed finite element approximation for temporal-spatial discretization, and explicit treatment for the interface terms and nonlinear terms. The proposed scheme is almost unconditionally stable and requires solving only the linear equation with constant coefficient at each time step. It can also penalize for lack of mass conservation and improve the accuracy. Finally, a series of numerical experiments are carried out to illustrate the stability and effectiveness of the proposed scheme.

中文翻译：

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基于 grad-div 稳定性的 Navier-Stokes-[公式省略]/Navier-Stokes-[公式省略] 方程的广义标量辅助变量方法


在本文中，基于 grad-div 稳定性，我们提出了一种广义标量辅助变量方法，用于求解由 Navier-Stokes-ω/Navier-Stokes-ω 方程控制的流体-流体相互作用问题。我们采用反向欧拉方案和混合有限元近似进行时空离散化，并对界面项和非线性项进行显式处理。所提出的方案几乎是无条件稳定的，只需要在每个时间步长求解系数恒定的线性方程。它还可以因缺乏质量守恒而受到惩罚并提高准确性。最后，进行了一系列数值实验，以验证所提方案的稳定性和有效性。