An efficient semi‐implicit temporal scheme for boundary‐layer vertical diffusion
Bibliographic record
Abstract
Time integration of the boundary‐layer vertical diffusion equation has been investigated. The nonlinearity associated with the diffusion coefficient makes the implicit approach impractical, while the use of an explicit scheme limits the stable time‐step sizes and consequently would be inefficient. By using a diagonally implicit Runge–Kutta scheme, a new approach has been proposed in which the diffusion coefficients at each internal stage are calculated by a weight‐averaged combination of solutions. Using the weight coefficient α offers more robust calculations due to involving implicit solutions and, as shown, it could improve the accuracy due to more engaging the explicit solutions. It has been found that the proposed semi‐implicit method is more accurate and computationally less expensive than the implicit scheme. Moreover, in terms of stability and accuracy improvement, the advantage of the proposed DIRK scheme, compared to the scheme proposed by Diamantakis et al. ( ), has been revealed, particularly for a highly nonlinear diffusion term.
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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 | 0.000 | 0.001 |
| 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 | 0.000 |
| 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 | 0.000 |
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 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".