A data-driven reduced-order model framework for predicting turbulent channel flows

The study of reduced-order models (ROMs) for flow fields is crucial in flow control, flow prediction, and digital twin applications. ROM provides a powerful tool for reducing the computational cost of simulating flow phenomena, making it indispensable in the aforementioned fields. Although various ROMs have been recently proposed, most are limited to simple flow structures with prominent flow features. The applicability and accuracy of existing methods remain limited in more complex flow scenarios. Therefore, we propose a novel data-driven ROM framework. This framework first extracts spatiotemporal evolution features of the flow field using proper orthogonal decomposition (POD). It then applies the K-means clustering algorithm to categorize the POD modes based on their frequency and constructs a long short-term memory prediction model for each cluster. In this case study, three-dimensional incompressible channel flows with varying domain sizes and Reynolds numbers were examined. The results demonstrate that the proposed model exhibits good statistical consistency with large eddy simulation for the prediction of various statistical properties and structures of velocity fields. Under the optimal hyperparameter settings, the model achieved minimum prediction errors of 5.6%, 3.8%, and 4.1% for the streamwise velocity components in the three channel flow examined cases. Furthermore, the model demonstrated superior accuracy compared with other methods for channel flow predictions within a similar computational time. Finally, the sensitivity of the model to different input-output time steps and the number of neurons was investigated.