We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for an implementation of the Leray model that combines a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. The main novelty of the proposed approach relies in applying spatial filtering both for the collection of the snapshots and in the reduced order model, as well as in considering the pressure field at reduced level. In both steps of the EF algorithm, velocity and pressure fields are approximated by using different POD basis and coefficients. For the reconstruction of the pressures fields, we use a pressure Poisson equation approach. We test our ROM on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number $0\le Re\le 100$. The accuracy of the reduced order model is assessed against results obtained with the full order model. For the 2D case, a parametric study with respect to the filtering radius is also presented.

我们为基于Leray模型的实现提出了一种基于正确正交分解（POD）-Galerkin的降阶模型（ROM），该模型结合了称为进化过滤器（EF）的两步算法和计算效率高的有限体积方法。所提出的方法的主要新颖之处在于在快照的收集和降阶模型中都应用了空间滤波，以及在降低的水平上考虑了压力场。在EF算法的两个步骤中，速度场和压力场都是通过使用不同的POD基础和系数来近似的。对于压力场的重建，我们使用压力泊松方程方法。我们在两个基准问题上测试ROM：以雷诺数通过圆柱体的2D和3D非稳态流动$0\le \mathrm{[R}Ë\le 100$。相对于使用完整订单模型获得的结果来评估降阶订单模型的准确性。对于2D情况，还介绍了有关滤波半径的参数研究。