滤波稳定化与涡粘模型之间的联系
A connection between filter stabilization and eddy viscosity models
AI总结：
本文证明了基于非线性微分滤波的不可压缩Navier-Stokes方程稳定化方法与LES中的涡粘模型等价，并分析了滤波性质，同时给出了投影法中滤波数值解收敛到DNS解的估计。
摘要：
最近，针对高雷诺数不可压缩Navier-Stokes方程的稳定化，提出了一种新方法，该方法基于离散格式每个时间步上解的非线性微分滤波。本文证明该稳定化等价于LES中的某种涡粘模型。这有助于对所需滤波性质进行更精细的分析和进一步理解。我们还考虑了滤波在投影（压力校正）方法中的应用，这是不可压缩流体方程时间积分的标准分裂算法。本文证明了滤波数值解收敛到相应DNS解的估计。
英文摘要：
Recently, a new approach for the stabilization of the incompressible Navier-Stokes equations for higher Reynolds numbers was introduced based on the nonlinear differential filtering of solutions on every time step of a discrete scheme. In this paper, the stabilization is shown to be equivalent to a certain eddy-viscosity model in LES. This allows a refined analysis and further understanding of desired filter properties. We also consider the application of the filtering in a projection (pressure correction) method, the standard splitting algorithm for time integration of the incompressible fluid equations. The paper proves an estimate on the convergence of the filtered numerical solution to the corresponding DNS solution.
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