FourNetFlows: An efficient model for steady airfoil flows prediction

Abstract: FourNetFlows, the abbreviation of Fourier Neural Network for Airfoil Flows, is an efficient model that provides quick and accurate predictions of steady airfoil flows. We choose the Fourier Neural Operator (FNO) as the backbone architecture and utilize OpenFOAM to generate numerical solutions of airfoil flows for training. Our results indicate that FourNetFlows matches the accuracy of the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) integrated with the Spalart-Allmaras turbulence model, one of the numerical algorithms. FourNetFlows is also used to predict flows around an oval whose shape is definitely different from samples in the training set. We note that both qualitative and quantitative results are consistent with the numerical results. Meanwhile, FourNetFlows solves thousands of solutions in seconds, orders of magnitude faster than the classical numerical method. Surprisingly, FourNetFlows achieves model flows with zero-shot super-resolution when it is trained under a lower resolution. And the inferring time is almost constant when the resolution of solutions is increasing.