Physics-informed neural networks for solving Reynolds-averaged Navierx2013Stokes equations

07/22/2021

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by   Hamidreza Eivazi, et al.

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Physics-informed neural networks (PINNs) are successful machine-learning methods for the solution and identification of partial differential equations (PDEs). We employ PINNs for solving the Reynolds-averaged Navierx2013Stokes (RANS) equations for incompressible turbulent flows without any specific model or assumption for turbulence, and by taking only the data on the domain boundaries. We first show the applicability of PINNs for solving the Navierx2013Stokes equations for laminar flows by solving the Falknerx2013Skan boundary layer. We then apply PINNs for the simulation of four turbulent-flow cases, i.e., zero-pressure-gradient boundary layer, adverse-pressure-gradient boundary layer, and turbulent flows over a NACA4412 airfoil and the periodic hill. Our results show the excellent applicability of PINNs for laminar flows with strong pressure gradients, where predictions with less than 1 also obtain very good accuracy on simulation results even for the Reynolds-stress components.