Physics-informed neural networks for solving Reynolds-averaged Navier$\unicode{x2013}$Stokes equations

Abstract

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 Navier$\unicode{x2013}$Stokes (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 Navier$\unicode{x2013}$Stokes equations for laminar flows by solving the Falkner$\unicode{x2013}$Skan 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% error can be obtained. For turbulent flows, we also obtain very good accuracy on simulation results even for the Reynolds-stress components.

Proc. 13th ERCOFTAC Symp. on Engineering Turbulence Modeling and Measurements (ETMM13), Rhodes, Greece, September 15-17, 2021

References in corpus (11)

• Flow over an espresso cup: Inferring 3D velocity and pressure fields from tomographic background oriented schlieren videos via physics-informed neural networks
• Uncovering near-wall blood flow from sparse data with physics-informed neural networks
• Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows
• Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning
• Applying deep reinforcement learning to active flow control in turbulent conditions
• Physics-guided deep learning framework for predictive modeling of the Reynolds stress anisotropy
• From coarse wall measurements to turbulent velocity fields through deep learning
• Physics-informed neural networks for imaging and parameter retrieval of photonic nanostructures from near-field data
• Convolutional-network models to predict wall-bounded turbulence from wall quantities
• Physics-informed deep-learning applications to experimental fluid mechanics
• Mapping Saturn using deep learning

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