• Achieved direct numerical simulation of lifting body model • Developed a spatiotemporal turbulence prediction model based on the Koopman operator • Enabled rapid prediction of high speed turbulent wall friction and heat flux Research on high-speed turbulent boundary layers is essential for drag reduction design in aerospace vehicles, and the emergence of artificial intelligence technologies has introduced an entirely new paradigm for such investigations. This paper develops a neural network architecture based on the Koopman operator for the temporal prediction of high-speed turbulent boundary layers. First, a direct numerical simulation of the lifting-body model was performed, yielding a windward region dataset for training and prediction with the neural operator model. Extensive qualitative and quantitative analyses demonstrate that the constructed Koopman operator model outperforms existing classical neural network and operator-based models in both memory consumption and training speed, while also achieving a substantial improvement in model interpretability. For turbulent boundary layers characterized by high-frequency features, the Koopman operator accurately captures small scale flow structures over short temporal intervals, while simultaneously achieving significant reductions in computational cost and memory requirements.
Zuo et al. (Sun,) studied this question.