Physics-informed neural networks for steady power-law fluid flows around a square cylinder in a two-dimensional channel

Physics-informed neural networks (PINNs) enable mesh-free solutions of partial differential equations (PDE) but can suffer from training stagnation or convergence to non-physical solutions in moderate-to-high Reynolds number non-Newtonian bluff-body flows. This study investigates steady confined channel flow around a square cylinder for power-law fluids and evaluates, within a data-free PINN framework (boundary and PDE residual constraints only), the effects of Fourier feature embedding and a re-initialization training strategy. Predictions are performed for Reynolds numbers Re=10, 40, and 100 and power-law indices n=0.5, 1.0, and 1.4, and are compared against benchmark computational fluid dynamics (CFD) results. Fourier features improve accuracy at low Reynolds numbers but can yield low-residual yet non-physical solutions at higher Reynolds numbers, manifested by windward stagnation point displacement and attenuation of predicted magnitudes. Re-initialization mitigates training stagnation and reduces errors but may induce non-physical wake deflection at the highest Reynolds number. These findings clarify how feature embedding and re-initialization affect PINN robustness for confined non-Newtonian flow simulations.