Convolution-compacted visiontransformers forprediction of localwall heat flux atmultiple Prandtlnumbers in turbulentchannel flow

Sammanfattning: Predicting wall heat flux accurately in wall-bounded turbulent flows is critical for a variety of engineering applications, including thermal management systems and energy-efficient designs. Traditional methods, which rely on expensive numerical simulations, are hampered by increasing complexity and extremly high computation cost. Recent advances in deep neural networks (DNNs), however, offer an effective solution by predicting wall heat flux using non-intrusive measurements derived from off-wall quantities. This study introduces a novel approach, the convolution-compacted vision transformer (ViT), which integrates convolutional neural networks (CNNs) and ViT to predict instantaneous fields of wall heat flux accurately based on off-wall quantities including velocity components at three directions and temperature. Our method is applied to an existing database of wall-bounded turbulent flows obtained from direct numerical simulations (DNS). We first conduct an ablation study to examine the effects of incorporating convolution-based modules into ViT architectures and report on the impact of different modules. Subsequently, we utilize fully-convolutional neural networks (FCNs) with various architectures to identify the distinctions between FCN models and the convolution-compacted ViT. Our optimized ViT model surpasses the FCN models in terms of instantaneous field predictions, learning turbulence statistics, and accurately capturing energy spectra. Finally, we undertake a sensitivity analysis using a gradient map to enhance the understanding of the nonlinear relationship established by DNN models, thus augmenting the interpretability of these models.