Super-resolution reconstruction of turbulent flows with a hybrid framework of attention

In a plethora of research endeavors concerning flow fields, acquiring high-resolution data is paramount. However, obtaining high-resolution turbulence data invariably requires substantial computational resources. Although super-resolution reconstruction of turbulent fields has emerged as a salient technique for detail extraction, conventional interpolation methods pose a significant challenge in reconstructing small-scale structures, often resulting in overly smooth outcomes. In this study, we propose a novel hybrid framework of spatially-adaptive feature attention (HSAFA) for the high-quality reconstruction of turbulent fields. This framework is characterized by the implementation of multidimensional feature fusion, which enhances the model's ability to capture details of turbulence. We rigorously applied the proposed model to datasets comprising laminar flow around a square cylinder and turbulent channel flows, with the reconstructed instantaneous velocity fields and statistics subjected to exhaustive and comparative analysis. Our findings demonstrate that HSAFA is capable of effectively reconstructing high-resolution turbulence fields from significantly low-resolution data, covering the range from laminar to turbulent flows.