Finite‐difference 4th‐order compact scheme for the direct numerical simulation of instabilities of shear layers
Bibliographic record
Abstract
Abstract An algorithm based on the 4th‐order finite‐difference compact scheme is developed and applied in the direct numerical simulations of instabilities of channel flow. The algorithm is illustrated in the context of stream function formulation that leads to field equation involving 4th‐order spatial derivatives. The finite‐difference discretization in the wall‐normal direction uses five arbitrarily spaced points. The discretization coefficients are determined numerically, providing a large degree of flexibility for grid selection. The Fourier expansions are used in the streamwise direction. A hybrid Runge–Kutta/Crank–Nicholson low‐storage scheme is applied for the time discretization. Accuracy tests demonstrate that the algorithm does deliver the 4th‐order accuracy. The algorithm has been used to simulate the natural instability processes in channel flow as well as processes occurring when the flow is spatially modulated using wall transpiration. Extensions to three‐dimensional situations are suggested. Copyright © 2005 John Wiley & Sons, Ltd.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".