Machine-learning-based simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator framework

TL;DR

The paper addresses fast, accurate prediction of strongly separated 3D turbulent flows over curved boundaries using a surrogate LES approach. It introduces HUFNO, a hybrid architecture that applies Fourier neural operators in periodic directions and a CNN-based U-Net in non-periodic directions, enabling efficient learning of both periodic and non-periodic flow dynamics. Across extensive tests on turbulent flows over periodic hills, HUFNO outperforms the original FNO and U-Net, and surpasses traditional Smagorinsky and WALE closures in velocity, Reynolds stresses, energy spectra, and wall-shear predictions, with substantially lower computational cost. The results demonstrate strong transferability to unseen initial conditions, hill shapes, Reynolds numbers, and 3D hill geometries, suggesting wide potential for rapid, accurate predictions of complex curved-boundary turbulence in engineering and geophysical applications.

Abstract

Simulating massively separated turbulent flows over bodies is one of the major applications for large-eddy simulation (LES). In the current work, we propose a machine-learning-based LES framework for the rapid simulation of turbulent flows over periodic hills using a hybrid U-Net and Fourier neural operator (HUFNO) framework. The newly proposed HUFNO model integrates the strengths of both the convolutional neural network (CNN) and Fourier neural operator (FNO) in a novel way that the FNO is applied in the periodic directions of the flow field while the non-periodicity is handled by the CNN-based U-Net framework. In the numerical tests, compared to the original FNO and the U-Net framework, the HUFNO model shows 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 invariant characteristics of velocity gradients, the wall stresses and the flow separation structures, with much lower computational cost. Importantly, the accuracy and efficiency are transferable to unseen initial conditions, Reynolds number and hill shapes, underscoring its great potentials for the fast prediction of strongly separated turbulent flows over curved boundaries.

Figures (15)

• Figure 1: The configurations of (a) Fourier neural operator (FNO); and (b) hybrid U-Net and Fourier neural operator (HUFNO).
• Figure 2: The computational domain of periodic hill flow: (a) 3D view; (b) varying shapes in 2D view.
• Figure 3: The influence of the channel width in the high-dimensional space on the training and testing losses at $Re=700$.
• Figure 4: The evolutions of the loss curves: (a) $Re=700$; (b) $Re=1400$; (c) $Re=5600$.
• Figure 5: The predicted turbulence statistics by different NN-based models: the first, second and third rows represent the results at $Re=700$, $1400$ and $5600$, respectively; the first, second and third columns represent $\langle u \rangle$, $\langle u'u' \rangle$ and $\langle u'v' \rangle$, respectively.