Hidden field discovery of turbulent flow over porous media using physics-informed neural networks

This study utilizes Physics-Informed Neural Networks (PINNs) to analyze turbulent flow passing over fluid-saturated porous media. The fluid dynamics in this configuration encompasses complex features, including leakage, channeling and pulsation at the pore-scale, which pose challenges for detailed flow characterization using conventional modeling and experimental approaches. Our PINNs model integrates (i) Reynolds Averaged Navier-Stokes (RANS) k-ε turbulence model within the PINNs framework, (ii) implementation of domain decomposition in regions exhibiting abrupt flow changes, and (iii) parameterization of the Reynolds number in the PINNs model. The domain decomposition method, distinguishing between non-porous and porous regions, enables turbulent flow reconstruction with reduced training dataset dependency. Furthermore, Reynolds number parameterization in the PINNs model facilitates the inference of hidden first and second-order statistics flow fields. The developed PINNs approach tackles both the reconstruction of turbulent flow fields (forward problem) and the prediction of hidden turbulent flow fields (inverse problem). For training the PINN algorithm, Computational Fluid Dynamics (CFD) data based on the RANS approach is deployed. The findings indicate that the parameterized domain-decomposed PINNs model can accurately predict flow fields while requiring fewer internal training datasets. For the forward problem, when compared to the CFD results, the relative L2 norm errors in PINNs predictions for streamwise velocity and turbulent kinetic energy are 5.44% and 18.90%, respectively. For the inverse problem, the predicted velocity magnitudes at the hidden low and high Reynolds numbers in the shear layer region show absolute relative differences of 8.55% and 4.39% compared to the CFD results, respectively.