非线性LES滤波的混合降阶模型
A Hybrid Reduced Order Model for nonlinear LES filtering
摘要：
我们开发了一个降阶模型（ROM）的大涡模拟（LES）的方法，结合了一个三步的算法称为进化过滤放松（EFR）与计算效率高的有限体积法。我们的ROM的主要新颖之处在于使用内的EFR算法的非线性，基于反卷积的指示函数，确定该领域的流动需要正规化。我们提出的ROM是一个混合投影/数据驱动的策略：一个经典的适当的正交分解Galerkin投影方法重建的速度和压力场和数据驱动的减少方法来近似的指示函数所使用的非线性微分滤波器。这种数据驱动技术基于径向基函数插值。我们测试我们的ROM方法的性能上的两个基准问题：二维和三维非定常流通过一个圆柱在雷诺数0 <= Re <= 100。ROM的准确性进行了评估与速度，压力，指示函数和时间演变的空气动力学系数的全阶模型获得的结果。
英文摘要：
We develop a Reduced Order Model (ROM) for a Large Eddy Simulation (LES) approach that combines a three-step algorithm called Evolve-Filter-Relax (EFR) with a computationally efficient finite volume method. The main novelty of our ROM lies in the use within the EFR algorithm of a nonlinear, deconvolution-based indicator function that identifies the regions of the domain where the flow needs regularization. The ROM we propose is a hybrid projection/data-driven strategy: a classical Proper Orthogonal Decomposition Galerkin projection approach for the reconstruction of the velocity and the pressure fields and a data-driven reduction method to approximate the indicator function used by the nonlinear differential filter. This data-driven technique is based on interpolation with Radial Basis Functions. We test the performance of our ROM approach on two benchmark problems: 2D and 3D unsteady flow past a cylinder at Reynolds number 0 <= Re <= 100. The accuracy of the ROM is assessed against results obtained with the full order model for velocity, pressure, indicator function and time evolution of the aerodynamics coefficients.
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