  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.
