Deep learning-based predictive modelling of transonic flow over an aerofoil

TL;DR

This work tackles the prediction of high-resolution, unsteady transonic flow over a NACA0012 aerofoil by learning a differentiable, rollout-enabled operator using an attention U‑Net. The model generalizes to unseen free-stream Mach numbers and even to inhomogeneous initial conditions, while enabling a global instability analysis by treating the network as a linearized operator around a time-averaged base flow. Key contributions include (i) a curriculum-based rollout training regime with input-noise augmentation, (ii) demonstration of accurate prediction of flow fields and aerodynamic statistics across multiple regimes, and (iii) a Jacobian-based spectral analysis that identifies dominant Kelvin–Helmholtz and shock-motion modes consistent with FFT observations. The approach yields substantial speedups over CFD simulations and provides a framework to interpret learned dynamics through classical stability concepts, with implications for flow control and optimization.

Abstract

Effectively predicting transonic unsteady flow over an aerofoil poses inherent challenges. In this study, we harness the power of deep neural network (DNN) models using the attention U-Net architecture. Through efficient training of these models, we achieve the capability to capture the complexities of transonic and unsteady flow dynamics at high resolution, even when faced with previously unseen conditions. We demonstrate that by leveraging the differentiability inherent in neural network representations, our approach provides a framework for assessing fundamental physical properties via global instability analysis. This integration bridges deep neural network models and traditional modal analysis, offering valuable insights into transonic flow dynamics and enhancing the interpretability of neural network models in flowfield diagnostics.

Figures (18)

• Figure 1: (a) Computational mesh with $1024\times128$ grid cells; (b) The contour of the y-component velocity at $M_{\infty}=0.825$ on the fine grids on the left column v.s. filtered one on coarse grids ($256\times64$) on the right column. The bottom shows the fields with the corresponding meshes.
• Figure 2: Typical flowfields in the training set.
• Figure 3: (a) Root mean square values of lift coefficients and (b) Statistically mean drag coefficients; shaded regions represent $\pm3$ standard deviations.
• Figure 4: Long-term $L_2$ errors measured using five large-network-size models (8.14M), each initialized with distinct random seeds.
• Figure 5: The flowfield from the inference at $M_{\infty}=0.755$ after 999 prediction steps.