Evaluating k–ω shear stress transport closure model in physics-informed neural network for turbulent channel flow

A physics-informed neural network (PINN) provides a mesh-free surrogate model that solves the governing partial differential equations (PDEs). In the present study, we develop a PINN for turbulent channel flow utilizing Reynolds-averaged Navier–Stokes (RANS) equations with a k–ω shear stress transport closure model and evaluate the effect of specific dissipation rate (ω) stiffness and numerical simulation data usage on the trained model performance. It is shown that the stiffness of ω near the wall is challenging for the PINN to learn, which can result in large prediction errors in the whole domain. The stiffness has the highest impact on reducing the residual of ω PDE and fitting the boundary condition of ω at the wall. A case study using a two-dimensional converging–diverging channel shows that using 250 interior reference data points (0.25% of simulation mesh points), the relative L2 errors between PINN prediction and RANS result reduce to around 5% for velocity and pressure, around 10% for the turbulent kinetic energy, and around 20% for the specific dissipation rate by removing the ω-PDE residual. Such a result indicates that the ω values in the flow field can be effectively learned from other PDEs and sparse interior reference data with stiff ω values near the wall.