Physically-consistent full-scale unsupervised reconstruction in turbulent flow dynamics
摘要
An advanced super-resolution reconstruction method for turbulent flows should be efficient, avoiding reliance on high-resolution data; reliable, strictly adhering to physical laws; and accurate, effectively reconstructing both small- and large-scale flow structures. To achieve these objectives, we developed TurbRec, an unsupervised, physically-consistent full-scale turbulent reconstruction model. This novel framework is designed to capture both high- and low-frequency information for precise reconstruction of small- and large-scale turbulent structures. TurbRec relies entirely on low-resolution inputs and governing equations, eliminating the need for high-resolution data and ensuring both efficiency and physical fidelity. Inspired by the multi-scale nature of turbulence and the energy cascade process, our approach integrates frequency-aware Fourier feature embeddings, capturing the full spectrum of turbulent frequencies and enhancing the model’s ability to represent intricate spectral details. To maintain physical consistency, we embed the governing equations within the super-resolution process and introduce a series of physics-motivated strategies, including segmented learning with overlapping windows, multi-scale normalization, and an enhanced residual learning network architecture. These innovations address known challenges in turbulent flow reconstruction, such as accurately predicting small-scale structures and ensuring smooth transitions across temporal boundaries. Numerical experiments demonstrate that TurbRec consistently outperforms traditional physics-informed neural networks in predicting instantaneous spatial flow structures, turbulent kinetic energy spectra, and various turbulent statistics.