Sparse learning model with embedded RIP conditions for turbulence super-resolution reconstruction

In practical engineering scenarios, constraints arising from sensor placement, quantity, and the limitations of current testing technologies often lead to turbulence data characterized by low resolution and irregular structures. Turbulence super-resolution reconstruction is crucial for extracting finer details from irregularly structured, low-resolution measurement data, thereby facilitating comprehensive flow field analyses. This article introduces a sparse learning model (Embedding Restricted Isometry Property Autoencoder (RIP-AE)) for achieving super-resolution reconstruction of flow fields by obtaining compressed representations and sparse transform domain information. In this model, we embed the Restricted Isometry Property (RIP) condition to ensure the effectiveness of compressed representations and sparse transform domains, thereby enhancing the super-resolution reconstruction accuracy of the model. To assess the performance of the RIP-AE model, we utilized data sets of flow around a cylinder at different Reynolds numbers generated by unsteady Reynolds-Averaged Navier–Stokes simulations. We sequentially validate the effectiveness of the RIP condition at different Reynolds numbers (ranging from 1,000 to 500,000) and compare the reconstruction results of the RIP-AE model with those of the downsampled skip-connection/multi-scale (DSC/MS) and MS-AE models under different sampling ratios. The results indicate that the RIP-AE model excels in terms of L2 relative error and demonstrates the capability to achieve high-precision flow field reconstruction even under high sampling ratios.