In recent years, grad-div stabilization has become a popular technique for improving the mass conservation of a solution to the incompressible Navier-Stokes equations (NSE). Grad-div stabilization can be easily implemented in any code that already uses the very common Taylor-Hood finite elements. In this paper we do a close review of the grad-div stabilized and modular grad-div stabilized NSE applied to a well-known benchmark problem: 2D flow around a cylindrical obstacle. We show that using current methods grad-div stabilization can change the calculated drag and lift coefficients. We will then suggest a remedy for the given test problem and verify our results by showing the grad-div parameters agree with the reference values and those calculated using Scott-Vogelius finite elements.

近年来，grad-div 稳定已成为一种流行的技术，用于改进不可压缩 Navier-Stokes 方程 (NSE) 解的质量守恒。Grad-div 稳定可以在任何已经使用非常常见的 Taylor-Hood 有限元的代码中轻松实现。在本文中，我们仔细回顾了应用于众所周知的基准问题的 grad-div 稳定和模块化 grad-div 稳定 NSE：围绕圆柱形障碍物的二维流动。我们表明，使用当前方法 grad-div 稳定可以改变计算出的阻力和升力系数。然后，我们将为给定的测试问题提出补救建议，并通过显示 grad-div 参数与参考值和使用 Scott-Vogelius 有限元计算的值一致来验证我们的结果。