Bibliographic record
Abstract
The false diffusions of six flux limiters were examined in a series of advection simulation experiments conducted for different flow directions and Courant numbers. The rate of deviation from the exact solution determines the false-diffusion coefficients that are defined by the Lagrangian diffusion equation. Occasional intervention by downgrading high-order schemes to a lower order produces a false-diffusion error that is linearly in proportion to the size of the computation grid. The dimensionless coefficient normalized by the grid size oscillates with time. The amplitude of the oscillations is evaluated as an indicator of computational instability. Some flux limiters, such as MINMOD, produce computationally stable results. However, the simulation by MINMOD is diffusive. Other flux limiters such as ULTRA-QUICK and ULTRA-CD are more accurate and not as diffusive, but computationally are not as stable. This study found that the false-diffusion coefficients of the flux limiters became independent of the Courant number when the fourth-order Runge−Kutta method was used for time integration. Using fourth-order time integration, the flux limiter SUPERBEE was nine times less diffusive than MINMOD, and 49 times less diffusive than the first-order upwind scheme.
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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 | 0.000 | 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 | 0.001 | 0.001 |
| Open science | 0.001 | 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".