First‐ and second‐order sensitivity equation methods for value and shape parameters
Bibliographic record
Abstract
Abstract This paper presents formulations of the sensitivity equation method (SEM) and applications to transient flow problems. Solutions are shown for both value and shape parameters using a three‐dimensional solution algorithm. Sensitivities are used for fast evaluation of the flow at nearby values of the parameters: the solution is approximated by a Taylor series in parameter space involving the flow sensitivities. The accuracy of nearby flows is much improved when second‐order sensitivities are used. We show how the sensitivity of the Strouhal number can be obtained from the flow sensitivities. Results are in agreement with the experimental correlation. The methodology is also applied to the flow past a cylinder in ground proximity. The proposed method is verified on a steady‐state problem by comparing the computed sensitivity with the actual change in the solution when a small perturbation is imposed on the shape parameter. We then investigate the ability of the SEM to anticipate the unsteady flow response to changes in the ground to cylinder gap. The approach properly reproduces the damping or amplification of the vortex shedding with a reduction or increase of the gap size. Copyright © 2008 Crown in the right of Canada. Published by John Wiley & Sons, Ltd.
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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 | 0.002 | 0.001 |
| 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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".