Continuous Eulerian and Lagrangian Sensitivities for the Design of Airfoils in Laminar Flow
Bibliographic record
Abstract
´This paper presents a gradient-based optimal design procedure using the Continuous Lagrangian Sensitivity equation method (CLSEM) and a NURBS representation of the geometry. First, the CLSEM provides a more accurate evaluation of the derivatives of the objective functions than our previous approach using a Continuous Eulerian Sensitivity Equation Method (CESEM a.k.a. SEM or CSEM). Since this sensitivity formulation leads directly to the material derivatives of the dependent variables of the flow, the computation of the gradients with respect to shape parameters is simple and direct. Second, the geometric representation of airfoils based on NURBS reduces the number of design variables needed to accurately represent a wing section and ensures good smoothness properties. Furthermore the NURBS representation of airfoils is compatible with most CAD systems. The resulting optimal design procedure is described and then verified using the Method of Manufactured Solutions. It is applied to the design of airfoils in laminar flow at low Reynolds numbers.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 source (direct Gemma or distilled Codex), 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".