Physics-Driven Learning of the Steady Navier-Stokes Equations using Deep Convolutional Neural Networks  

作　　者：Hao Ma Yuxuan Zhang Nils Thuerey Xiangyu Hu Oskar J.Haidn 

机构地区：[1]Department of Aerospace and Geodesy,Technical University of Munich,85748 Garching,Germany [2]Beijing Aerospace Propulsion Institute,100076,Beijing,China [3]Technical University of Munich,85748,Garching,Germany [4]Department of Mechanical Engineering,Technical University of Munich,85748 Garching,Germany

出　　处：《Communications in Computational Physics》2022年第8期715-736,共22页计算物理通讯（英文）

基　　金：Hao Ma(No.201703170250)and Yuxuan Zhang(No.201804980021)are supported by China Scholarship Council when they conduct the work this paper represents.

摘　　要：Recently,physics-driven deep learning methods have shown particular promise for the prediction of physical fields,especially to reduce the dependency on large amounts of pre-computed training data.In this work,we target the physicsdriven learning of complex flow fields with high resolutions.We propose the use of Convolutional neural networks(CNN)based U-net architectures to efficiently represent and reconstruct the input and output fields,respectively.By introducingNavier-Stokes equations and boundary conditions into loss functions,the physics-driven CNN is designed to predict corresponding steady flow fields directly.In particular,this prevents many of the difficulties associated with approaches employing fully connected neural networks.Several numerical experiments are conducted to investigate the behavior of the CNN approach,and the results indicate that a first-order accuracy has been achieved.Specifically for the case of a flow around a cylinder,different flow regimes can be learned and the adhered“twin-vortices”are predicted correctly.The numerical results also show that the training for multiple cases is accelerated significantly,especially for the difficult cases at low Reynolds numbers,and when limited reference solutions are used as supplementary learning targets.

关 键 词：Deep learning physics-drivenmethod convolutional neural networks Navier-Stokes equations 

分 类 号：O17[理学—数学]