A transformer-based neural operator for large-eddy simulation of turbulence
arxiv(2024)
Abstract
Predicting the large-scale dynamics of three-dimensional (3D) turbulence is
challenging for machine learning approaches. This paper introduces a
transformer-based neural operator (TNO) to achieve precise and efficient
predictions in the large-eddy simulation (LES) of 3D turbulence. The
performance of the proposed TNO model is systematically tested and compared
with classical sub-grid scale (SGS) models, including the dynamic Smagorinsky
model (DSM) and the dynamic mixed model(DMM), as well as the original Fourier
neural operator (FNO) model, in homogeneous isotropic turbulence (HIT) and
free-shear turbulent mixing layer. The numerical simulations comprehensively
evaluate the performance of these models on a variety of flow statistics,
including the velocity spectrum, the probability density functions (PDFs) of
vorticity, the PDFs of velocity increments, the evolution of turbulent kinetic
energy, and the iso-surface of the Q-criterion. The results demonstrate that
the TNO model exhibits better accuracy than the DSM, DMM, and FNO models in
both HIT and the turbulent mixing layer. Moreover, the TNO model has fewer
parameters than the FNO model and enables long-term stable predictions, which
the FNO model cannot achieve. Besides, the proposed TNO model is much faster
than traditional LES with DSM and DMM models, showing great potential in
tackling 3D nonlinear engineering problems.
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