Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations

Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations. We employ PINNs solving Reynolds-averaged Navier–Stokes equations incompressible turbulent flows without any specific model or assumption turbulence by taking only data on domain boundaries. first show applicability laminar Falkner–Skan boundary layer. then apply simulation four turbulent-flow cases, i.e., zero-pressure-gradient layer, adverse-pressure-gradient over a NACA4412 airfoil periodic hill. Our results excellent with strong pressure gradients, where predictions less than 1% error can be obtained. For flows, we also obtain very good accuracy even Reynolds-stress components.