Flow field modeling of airfoil based on convolutional neural networks from transform domain perspective

For complex flow problems such as wall-bounded turbulence with multi-scale and strongly nonlinear characteristics, the non-orthogonal and non-uniform meshes commonly used in numerical simulation limit the direct use of Convolutional Neural Networks (CNNs). The flow field is usually projected onto a uniform Cartesian mesh to use the convolution operation, which inevitably leads to the problem of missing information about the turbulent flow field in the near-wall region. To address this limitation, a method is proposed for flow field modeling using CNN from the perspective of the transform domain. Specifically, the flow field is transformed from the non-uniform physical plane to the uniform computational plane. From the view of the transform domain, the flow governing equations will naturally generate variables used to characterize the geometry through the coordinate transformation without the need to design specific features. Moreover, since the computational plane is uniform and orthogonal, the convolution can be used directly without interpolation preprocessing. For the case of shape-based flow field modeling of the 2D airfoil and 3D wing under high Reynolds number conditions, the velocity and pressure of the turbulent boundary layer can be predicted very well by this method, even in the discontinuous shock wave region. In addition, the pros and cons of two different but common modeling frameworks represented by CNN and proper orthogonal decomposition (POD) are presented. The modeling error of CNN is one order of magnitude smaller than that of POD, and the relative error of the integral force of CNN is less than 1%. This work shows that the proposed method has significant advantages of high accuracy and interpretability, and provides an efficient solution for parameter space research.