论文标题
通过神经网络提高湍流模型的准确性
Improving accuracy of turbulence models by neural network
论文作者
论文摘要
简单结构的神经网络用于构建用于大涡模拟（LES）的湍流模型。通过均质各向同性湍流的直接数值模拟（DNS）获得的数据用于训练神经网络。结果表明，两种方法可有效提高模型的准确性：用于训练和添加速度的二阶导数的加权数据对输入变量。结果，获得了较大的滤波器宽度，确切的亚网格尺度应力与通过神经网络的预测之间的高相关性。对于滤波器宽度48：8ηand97：4η的相关系数约为0：9和0：8，其中是kolmogorov量表。神经网络建立的模型接近但与梯度模型不相同。具有神经网络模型的LE是针对均匀的各向同性湍流和泰勒绿色涡流的初始问题问题的。通过神经网络模型获得的结果与过滤的DNS的结果是合理吻合的。但是，由于神经网络模型在正交转换下不具有严格的对称性，因此后一个问题中的对称性被打破了。
Neural networks of simple structures are used to construct a turbulence model for large-eddy simulation (LES). Data obtained by direct numerical simulation (DNS) of homogeneous isotropic turbulence are used to train neural networks. It is shown that two methods are effective for improvement of accuracy of the model: weighting data for training and addition of the second-order derivatives of velocity to the input variables. As a result, high correlation between the exact subgrid scale stress and the prediction by the neural network is obtained for large filter width; the correlation coefficient is about 0:9 and 0:8 for filter widths 48:8ηand 97:4η, respectively, where ηis the Kolmogorov scale. The models established by neural networks are close to but not identical with the gradient models. LES with the neural network model is performed for the homogeneous isotropic turbulence and the initial-value problem of the Taylor-Green vortices. The results obtained with the neural network model are in reasonable agreement with those of the filtered DNS. However, symmetry in the latter problem is broken since the neural network model does not possess rigorous symmetry under orthogonal transformations.
