Spectral algorithm for the analysis of flows in grooved channels
Bibliographic record
Abstract
SUMMARY A grid‐less, spectrally accurate algorithm for the analysis of flows in grooved channels is presented. The algorithm is based on the immersed boundary conditions concept, where the boundary conditions are submerged inside the computational domain and are treated as internal constraints. When grooves' ridges are orthogonal to the flow direction (transverse grooves), the flow remains two‐dimensional. As the grooves rotate away from this direction, the flow becomes three‐dimensional. An auxiliary coordinate system is defined in such a way that one of its axes is aligned with the grooves. It is shown that the governing equations expressed in this system decouple into a two‐dimensional flow across the grooves and a flow in the direction along the grooves, resulting in improved solution efficiencies. Fourier series are used for discretization in the direction transverse to the grooves and Chebyshev expansions for the direction across the channel. Special solvers that take advantage of the matrix structure have been implemented providing a significant acceleration of computation and reduction of memory requirements. Various tests have been conducted in order to illustrate the performance of the algorithm, to show its spectral accuracy and to characterize the effects of various numerical and physical parameters. Copyright © 2011 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 | 0.000 |
| Bibliometrics | 0.001 | 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) | 0.003 | 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".