Neural Network for Subgrid Turbulence Modeling for Large Eddy Simulations

TL;DR

This work tackles the closure problem in LES by learning a data-driven SGS closure that reproduces the effects of unresolved scales on the resolved flow. It builds an end-to-end workflow: generating high-fidelity DNS data for a Taylor–Green Vortex, constructing a reduced representation via a block reduction, and training a deep MLP to predict the deviatoric SGS stress $\tau_{ij}^d$ in a priori mode. The learned closure is then integrated into OpenFOAM as a CFD-AI coupling, with explicit handling of the SGS contribution in the momentum equations through $D_{\text{eff}}$ and $\nu_{\text{eff}}$, enabling a posteriori simulations. The results demonstrate strong a priori performance across laminar and turbulent phases, and the paper outlines a path toward robust, industrially applicable closures using more expressive architectures and physics-informed strategies.

Abstract

When simulating multiscale systems, where some fields cannot be fully prescribed despite their effects on the simulation's accuracy, closure models are needed. This phenomenon is observed in turbulent fluid dynamics, where Large Eddy Simulations (LES) depict global behavior while turbulence modeling introduces dissipation correspondent to smaller sub-grid scales. Recently, scientific machine learning techniques have emerged to address this problem by integrating traditional (physics-based) equations with data-driven (machine-learned) models, typically coupling numerical solvers with neural networks. This work presents a comprehensive workflow, encompassing high-fidelity data generation and post-processing, a priori learning, and a posteriori testing, where data-driven models enrich differential equations.

Figures (4)

• Figure 1: Effective energy dissipation per unit time for the original simulations --- our DNS, the DNS reference from Brachet, and our LES with Smagorinsky turbulence modeling. For the latter, the dissipation due to the turbulence model is also plotted.
• Figure 2: Norm of the filtered field $\Bar{u}$ --- low resolution set at 64. The image represents a cut at the origing according the x-axis at 7 seconds of the TGV simulation.
• Figure 3: Effective energy dissipation per unit time for original and post-processed simulations --- our DNS and the reduced simulations. The latter were achieved through a reduction operator $A: u \mapsto \bar{u}$ and include different turbulence models (Smagorinsky and \ref{['eq:tau']}), with their respective dissipation contributions also plotted.
• Figure 4: Evolution of error metrics (MAE and R2 score) over time in a priori, testing setting for the 10 seconds of the TGV experiment. The data originates from a DNS, processed through a reduction operator $A: u \mapsto \bar{u}$.