论文标题
统一的数据同化和湍流建模方法，用于高雷诺数的分离流量
A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers
论文作者
论文摘要
近年来，由深神经网络（DNN）代表的机器学习方法已成为湍流建模的新范式。但是，在高雷诺数字的情况下，仍然存在一些瓶颈，包括缺乏高保真数据以及湍流模型耦合过程中的收敛性和稳定性问题和赎金求解器。在本文中，我们提出了一种改进的集合Kalman倒置方法，作为在高雷诺数下分离流量的统一数据同化和湍流建模方法。根据给定的实验表面压力系数在RANS方程与DNN Eddy-Viscosity模型之间相互耦合的框架中，根据给定的实验表面压力系数优化了DNN的可训练参数。这样，将数据同化和模型训练合并为一个步骤，以使高保真湍流模型有效地与实验非常吻合。该方法的有效性通过在高雷诺数下的机翼围绕机翼（S809）分离的情况来验证。结果表明，通过连接的几乎没有实验状态的联合同化，我们可以以不同的攻击角度将湍流模型很好地推广到附着和分离的流动。与传统的SA模型相比，高攻击角度的升力系数误差显着减少了三倍以上。获得的模型在稳定性和鲁棒性方面也表现良好。
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the convergence and stability problem in the coupling process of turbulence models and the RANS solvers. In this paper, we propose an improved ensemble kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. The trainable parameters of the DNN are optimized according to the given experimental surface pressure coefficients in the framework of mutual coupling between the RANS equations and DNN eddy-viscosity models. In this way, data assimilation and model training are combined into one step to get the high-fidelity turbulence models agree well with experiments efficiently. The effectiveness of the method is verified by cases of separated flows around airfoils(S809) at high Reynolds numbers. The results show that through joint assimilation of vary few experimental states, we can get turbulence models generalizing well to both attached and separated flows at different angles of attack. The errors of lift coefficients at high angles of attack are significantly reduced by more than three times compared with the traditional SA model. The models obtained also perform well in stability and robustness.
