Assimilating mean velocity fields of a shockwave–boundary layer interaction from background-oriented schlieren measurements using physics-informed neural networks

We propose a novel method to reconstruct mean velocity fields of turbulent shockwave–boundary layer interactions (SBLIs) from background-oriented schlieren (BOS) measurement data using physics-informed neural networks (PINNs). By embedding the compressible Reynolds-Averaged Navier–Stokes equations into the PINN loss function, we recover a full set of physical variables from only the density gradient as training data. This technique has the potential to generate velocity fields similar to particle image velocimetry (PIV) results from usually simpler planar BOS measurements, at the cost of some computational resources. We analyze our method's capabilities on two oblique SBLI cases: a high-fidelity Mach 2.28 direct numerical simulation dataset for validation and a Mach 2.0 wind tunnel experiment. We demonstrate the positive impact of different wall boundary constraints such as the wall shear stress and pressure distribution for enhancing the PINN's convergence toward physically accurate solutions. The predicted fields are compared with experimental PIV and other point measurements, while we discuss the accuracy, limitations, and broader implications of our approach for SBLI research.