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.

中文翻译：

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具有嵌入式 RIP 条件的稀疏学习模型用于湍流超分辨率重建

在实际工程场景中，由于传感器放置、数量的限制以及当前测试技术的限制，往往会导致湍流数据分辨率低、结构不规则。湍流超分辨率重建对于从不规则结构、低分辨率测量数据中提取更精细的细节至关重要，从而促进全面的流场分析。本文介绍了一种稀疏学习模型（Embedding Restricted Isometry Property Autoencoder (RIP-AE)），通过获取压缩表示和稀疏变换域信息来实现流场的超分辨率重建。在该模型中，我们嵌入了受限等距属性（RIP）条件，以确保压缩表示和稀疏变换域的有效性，从而提高模型的超分辨率重建精度。为了评估 RIP-AE 模型的性能，我们利用了由非稳态雷诺平均纳维-斯托克斯模拟生成的不同雷诺数下圆柱体周围流动的数据集。我们依次验证了 RIP 条件在不同雷诺数（范围从 1,000 到 500,000）下的有效性，并将 RIP-AE 模型的重建结果与下采样跳跃连接/多尺度 (DSC/MS) 和 MS 的重建结果进行比较-不同采样率下的AE模型。结果表明，RIP-AE模型在L2相对误差方面表现出色，即使在高采样率下也能实现高精度流场重建。