Physics-Informed Super-Resolution of Turbulent Channel Flows via Three-Dimensional Generative Adversarial Networks

For a few decades, machine learning has been extensively utilized for turbulence research. The goal of this work is to investigate the reconstruction of turbulence from minimal or lower-resolution datasets as inputs using reduced-order models. This work seeks to effectively reconstruct high-resolution 3D turbulent flow fields using unsupervised physics-informed deep learning. The first objective of this study is to reconstruct turbulent channel flow fields and verify these with respect to the statistics. The second objective is to compare the turbulent flow structures generated from a GAN with a DNS. The proposed deep learning algorithm effectively replicated the first- and second-order statistics of turbulent channel flows of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mi>τ</mi></msub><mo>=</mo></mrow></semantics></math></inline-formula> 180 within a 2% and 5% error, respectively. Additionally, by incorporating physics-based corrections to the loss functions, the proposed algorithm was also able to reconstruct <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>λ</mi><mn>2</mn></msub></semantics></math></inline-formula> structures. The results suggest that the proposed algorithm can be useful for reconstructing a range of 3D turbulent flows given computational and experimental efforts.