A spectral/finite‐difference approach for narrow‐channel flow with inertia
Bibliographic record
Abstract
Abstract A hybrid spectral/finite‐difference scheme is proposed to determine the inertial flow inside narrow channels. The flow field is represented spectrally in the depthwise direction, which together with the Galerkin projection lead to a system of equations that are solved using a variable step finite difference discretization. The method is particularly effective for non‐linear flow, and its validity is here demonstrated for a flow with inertia. The problem is closely related to high‐speed lubrication flow. The validity of the spectral representation is assessed by examining the convergence of the method, and comparing with the fully two‐dimensional finite‐volume solution (FLUENT), and the widely used depth‐averaging method from shallow‐water theory. It is found that a low number of modes are usually sufficient to secure convergence and accuracy. Good agreement is obtained between the low‐order description and the finite‐volume solution at low to moderate modified Reynolds number. The depth‐averaging solution is unable to predict accurately (qualitatively and quantitatively) the high‐inertia flow. The influence of inertia is examined on the flow. Copyright © 2003 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 | 0.001 | 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 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".