A hybrid U-Net and Fourier neural operator framework for the fast prediction of turbulent flows with mixed periodic and non-periodic boundary conditions

Accurate and efficient predictions of three-dimensional (3D) turbulent flows are of significant importance in the fields of science and engineering. In the current work, we propose a hybrid U-Net and Fourier neural operator (HUFNO) method, tailored for mixed periodic and non-periodic boundary conditions which are often encountered in complex turbulence problems. The HUFNO model is tested in the large-eddy simulation (LES) of 3D periodic hill turbulence featuring strong flow separations. Compared to the original Fourier neural operator (FNO) and the convolutional neural network (CNN)-based U-Net framework, the HUFNO model has a higher accuracy in the predictions of the velocity field and Reynolds stresses. Further numerical experiments in the LES show that the HUFNO framework outperforms the traditional Smagorinsky (SMAG) model and the wall-adapted local eddy-viscosity (WALE) model in the predictions of the turbulence statistics, the energy spectrum, the wall stresses and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions and hill shapes, underscoring its great potentials for the fast prediction of strongly separated turbulent flows over curved boundaries.