Energy-Conserving Neural Network Closure Model for Long-Time Accurate and Stable LES
This addresses the problem of unreliable long-time LES for turbulence modeling, offering a more stable and physically consistent closure model, though it is incremental in improving existing machine learning approaches.
The paper tackled the instability and physical inconsistency of machine learning-based closure models for Large Eddy Simulation (LES) by developing a skew-symmetric neural architecture that enforces stability and conserves mass, momentum, and energy. The result showed that this model remained stable across all tests, outperforming the Smagorinsky model in unseen scenarios, though with increased dissipation.
Machine learning-based closure models for LES have shown promise in capturing complex turbulence dynamics but often suffer from instabilities and physical inconsistencies. In this work, we develop a novel skew-symmetric neural architecture as closure model that enforces stability while preserving key physical conservation laws. Our approach leverages a discretization that ensures mass, momentum, and energy conservation, along with a face-averaging filter to maintain mass conservation in coarse-grained velocity fields. We compare our model against several conventional data-driven closures (including unconstrained convolutional neural networks), and the physics-based Smagorinsky model. Performance is evaluated on decaying turbulence and Kolmogorov flow for multiple coarse-graining factors. In these test cases we observe that unconstrained machine learning models suffer from numerical instabilities. In contrast, our skew-symmetric model remains stable across all tests, though at the cost of increased dissipation. Despite this trade-off, we demonstrate that our model still outperforms the Smagorinsky model in unseen scenarios. These findings highlight the potential of structure-preserving machine learning closures for reliable long-time LES.