Development of a Data-Driven Wall Model for Separated flows
Bibliographic record
Abstract
Large Eddy Simulations (LES) are of increasing interest for turbomachinery design since they provide a more reliable prediction of flow physics and component behavior. However, they remain prohibitively expensive at high Reynolds numbers or actual complex geometries. Most of the cost is associated with the resolution of the boundary layer, and therefore, to save computational resources, wall-modeled LES (wmLES) has become a valued tool. However, wall models are not yet reliable in predicting the complex flow configurations occurring in turbomachinery passages. Most existing analytical wall models assume the flow to be fully turbulent, attached, flow aligned, and near-equilibrium. These assumptions no longer hold when different flow regimes and complex flow features coexist. Although significant progress has been made in recent years (e.g., non-equilibrium models using pressure gradients), they have not always brought a clear benefit for such realistic flows. This paper proposes an innovative data-driven wall model to treat separated flows. Among the many possibilities to solve this complex regression problem, deep neural networks have been selected for their universal approximation capabilities~\cite{hornik_approximation_1991}. In the present framework, the two-dimensional periodic hill problem is selected as a reference test case featuring the separation of a fully turbulent boundary layer. Gaussian Mixture Neural networks (GMN) and Convolutional Neural Networks (CNN) combined with a self-attention layer~\cite{Vaswani_sel_attention_2017} are trained to predict the wall-parallel components of the wall shear stress using instantaneous flow quantities and geometric parameters. The \textit{a priori} and \textit{a posteriori} validation of such data-driven wall models on the periodic hill problem will be presented.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.043 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".