Finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements: plane Poiseuille flow
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Bibliographic record
Abstract
Abstract This paper presents a comprehensive review of the numerical techniques used during the past half century and their accuracy in hydrodynamic stability analysis of plane parallel flows. The paper also describes a finite element solution of the Orr–Sommerfeld equation using high precision Hermite elements. A stability analysis technique is performed by imposing an infinitesimal perturbation to the laminar base flow to determine the thresholds of neutral instabilities or the growth rate of the perturbation for any Reynolds and wave numbers. Validation of the present numerical technique is performed for plane Poiseuille flow. The numerical results, obtained with uniform and nonuniform meshes, show excellent agreement with the most accurate results available in the literature. Copyright © 2004 John Wiley & Sons, Ltd.
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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 | 0.001 | 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 | 0.000 | 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 it