Two dimensional vertically averaged and moment equations for rapidly varied flows
Bibliographic record
Abstract
The classical depth averaged De St. Venant equations, which are used for most of the computational models in open channels, are based on the fundamental assumptions of uniform velocity and hydrostatic pressure distributions. They are thus limited in their applicability to cases where vertical details are not of importance. Alternative two-dimensional vertically averaged and moment equations are developed, by a moment weighted residual method from the fundamental 3D Reynolds equations, to account for problems where more vertical details are significant and essential. The proposed model is applied to rapidly varied flow problems involved in open channel flow. These problems include flow in channel transitions with rapid contraction and/or expansion and flow over a hemispherical hump. Linear distribution shapes are proposed for the horizontal velocity components, while quadratic distribution shapes are considered for vertical velocity and pressure. The implicit Petrov-Galerkin finite element scheme is used in these simulations. A good agreement is attained. In addition, the obtained results show that more details are gained and the flow is better represented by the proposed model compared to the classical De St. Venant model.
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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 | 0.001 | 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 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".