Numerical comparison of Bhatnagar–Gross–Krook models with proper Prandtl number
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Bibliographic record
Abstract
While the standard Bhatnagar–Gross–Krook (BGK) model leads to the wrong Prandtl number, the BGK model with velocity dependent collision frequency as well as the ellipsoidal statistical BGK (ES-BGK) model can be adjusted to give its proper value of 2/3. In this paper, the BGK model with velocity dependent collision frequency is considered in some detail. The corresponding thermal conductivity and viscosity are computed from the Chapman–Enskog method, and several velocity-dependent collision frequencies are introduced which all give the proper Prandtl number. The models are tested for Couette flow, and the results are compared to solutions obtained with the ES-BGK model, and the direct simulation Monte Carlo method. The simulations rely on a numerical scheme that ensures positivity of solutions, conservation of moments, and dissipation of entropy. The advantages and disadvantages of the various BGK models are discussed.
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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 | 0.000 | 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 it