A priori assessment of nonlocal data-driven wall modeling in large eddy simulation

Abstract

In the present study, a priori assessment is performed on the ability of the convolutional neural network (CNN) for wall-modeling in large eddy simulation. The data used for the training process are provided by the direct numerical simulation (DNS) of the turbulent channel flow. Initially, a study is carried out on the input choices of CNN, and the effect of different flow parameters on establishing a wall model is investigated. Then, the influence of the wall-normal distance on the established data-driven wall model is studied by choosing the CNN input data from two regions of the inner layer (y+>10,y/δ<0.1) and the logarithmic layer. The performance of the obtained CNN wall models based on the inputs from the two regions is further investigated by feeding the network with the data outside the training range. In the next step, the models are tested under various conditions, including a different grid size and a higher Reynolds number. The results show that the models using the inner layer (excluding y+≤10) data as the CNN input have better accuracy in establishing a wall model compared to the models based on the input data in the logarithmic layer, especially when implemented outside the training range. After optimizing the hyperparameters of CNN, a high correlation coefficient of 0.9324 is achieved between the wall shear stress calculated using the filtered DNS data and predicted by the best CNN wall model, which is trained using the data in the inner layer, excluding y+≤10. The performance of the CNN wall model is also compared with the existing wall-stress models, and it is shown that the CNN wall model has better accuracy in establishing a wall model. Additionally, the CNN wall model is shown to have good performance when applied to a different grid size or a higher Reynolds number.