Physics-informed neural networks for transonic flow around a cylinder with high Reynolds number

The physics-informed neural network (PINN) method is extended to learn and predict compressible steady-state aerodynamic flows with a high Reynolds number. To better learn the thin boundary layer, the sampling distance function and hard boundary condition are explicitly introduced into the input and output layers of the deep neural network, respectively. A gradient weight factor is considered in the loss function to implement the PINN methods based on the Reynolds averaged Navier-Stokes (RANS) and Euler equations, respectively, denoted as PINN-RANS and PINN-Euler. Taking a transonic flow around a cylinder as an example, these PINN methods are first verified for the ability to learn complex flows and then are applied to predict the global flow based on a part of physical data. When predicting the global flow based on velocity data in local key regions, the PINN-RANS method can always accurately predict the global flow field including the boundary layer and wake, while the PINN-Euler method can accurately predict the inviscid region. When predicting the subsonic and transonic flows under different freestream Mach numbers (Ma(infinity )= 0.3-0.7), the flow fields predicted by both methods avoid the inconsistency with the real physical phenomena of the pure data-driven method. The PINN-RANS method is insufficient in shock identification capabilities. Since the PINN-Euler method does not need the second derivative, the training time of PINN-Euler is only 1/3 times that of PINN-RANS at the same sampling point and deep neural network.