Overview
A differentiable hybrid neural-CFD framework, termed Hybrid-Joint, has been developed for wall-modelled large-eddy simulation (WMLES). This framework focuses on the coupled learning of subgrid-scale (SGS) and wall closures within a differentiable flow solver. The training process utilizes only low-order statistics as targets, and every operation within the framework is differentiable. This differentiability allows for the back-propagation of gradients of the training loss through the coupled solver, enabling consistent optimization of both neural closures against the flow field.
Research Context
Conventional WMLES approaches typically treat the SGS closure, wall closure, and numerical discretization as independent components. However, their effects are inherently coupled through the same resolved flow field. This independence in treatment can lead to inconsistencies and limitations in the accuracy and generalizability of WMLES models. The research addresses this by proposing a framework where these coupled effects are learned jointly, rather than in isolation or through offline fitting, to better capture their intricate interactions.
Approach
The Hybrid-Joint framework employs a differentiable flow solver. Within this solver, both the SGS and wall closures are designed as composed neural operators. Each neural operator consists of a trainable neural network followed by a fixed differentiable layer. This design ensures that the structure of the conventional counterparts of these closures is preserved, meaning the neural network learns only the functions left undetermined by the conventional form. The differentiability throughout the entire system allows gradients from the training loss to propagate backward through the coupled solver. This enables the simultaneous optimization of both neural closures against the flow field, using low-order statistics as the training objective. The framework was demonstrated on a zero-pressure-gradient turbulent boundary layer, and a posteriori tests were conducted across a range of Reynolds numbers ($Re_\theta = 600-6500$), varying computational domains, and different mesh resolutions.
Findings
- The Hybrid-Joint framework demonstrated superior performance compared to existing WMLES baselines.
- The model exhibited strong extrapolation capabilities, performing effectively at Reynolds numbers more than four times higher than the maximum Reynolds number encountered during training.
- It successfully transferred to grids and computational domains that were not part of the training dataset.
- The model recovered a logarithmic mean-velocity region, a characteristic feature of turbulent boundary layers, even though this behavior was not imposed by the wall closure within the framework.
- Accurate reproduction of resolved energy spectra was achieved, despite spectral information being explicitly excluded from the training objective.
- Ablation studies indicated that learning either the SGS closure or the wall closure in isolation was insufficient to achieve the full set of statistical reproductions.
- Joint optimization of both closures was found to be necessary to recover the complete set of statistics, thereby confirming the coupled nature of SGS closure, wall closure, and discretization, and the necessity of their joint training.
- Once trained, the closures could be reused across all tested cases without requiring retraining, allowing the training cost to be amortized over multiple deployments.
Why This Matters
The joint learning approach for SGS and wall closures within a differentiable flow solver offers a method to enhance the accuracy and robustness of wall-modelled large-eddy simulations. The ability of the trained closures to extrapolate to higher Reynolds numbers and transfer to different computational setups without retraining suggests potential for wider applicability in fluid dynamics research and engineering simulations. The findings underscore the importance of considering the coupled nature of different model components in complex fluid simulations for more accurate predictions.