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

By Hamidreza Eivazi, Mojtaba Tahani, Philipp Schlatter, Ricardo Vinuesa. The Physics of Fluids, 2021

445 citations recorded by the source corpus.

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-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-Stokes equations for laminar flows by solving the Falkner-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 an 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.

Subfields: Aerospace Engineering, Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0681f84e7edb02c6dd3720de59be14ad2ae3c78d

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Citations in the corpus

Enhancing computational fluid dynamics with machine learning (2021, methodology): “In fact, PINNs are being used for turbulence modeling [143] (solving the RANS equations without the need of a model for the Reynolds stresses), for developing ROMs [144], for dealing with noisy data [145] and for accelerating traditional solvers, for instance by means of solving the Poisson…”
PDEBENCH: An Extensive Benchmark for Scientific Machine Learning (2022, methodology): “For instance, data-driven ML methods are useful when observations are noisy or the underlying physical model is not fully known or deﬁned [11].”