Using Physics Informed Neural Network (PINN) to Improve a k-omega Turbulence Model

Paper in proceeding, 2025

The Wilcox k-omega turbulence model predicts turbulent boundary layers well, both fully-developed channel flows and flat-plate boundary layers. However, it predicts too low a turbulent kinetic energy. This is a feature it shares with most other two-equation turbulence models. When comparing the terms in the k equations with DNS data it is found that the production and dissipation terms are well predicted but the turbulent diffusion is not. In the present work the poor modeling of the turbulent diffusion is improved by making the turbulent diffusion constant, sigma_k, a function of y/\delta.By taking the production, the dissipation terms as well as the turbulent kinetic energy from DNS channel flow data, the k equation is turned into an ordinary differential equation for the turbulent viscosity which is solved using Physics Informed Neural Network (PINN). In order to not change the predicted turbulent viscosity -- which is well predicted by the standard Wilcox k-omega turbulence model -- a new function is added to the dissipation term and the destruction term in the omega equation. The new model, called the k-omega NN model, is shown to produce excellent velocity and turbulent kinetic profiles in channel flow at Re_tau = 2 000, Re_tau = 5 200, Re_tau = 10 000 as well as in flat-plate boundary layer flow. The Python PINN script and the pyCALC-RANS code can be downloaded (Davidson, 2025).