Conservative Formulation for Natural Open Channels and Finite-Element Implementation
Bibliographic record
Abstract
This investigation considers an approximate formulation of the St. Venant equations for natural channels, in which the fully conservative form is developed by revising the boundary pressure term accounting for the topographic variation in the momentum equation. As such a formulation has the potential to enhance the performance of existing models used in practice, the accuracy implications for this approximate formulation are examined using an error analysis for a simplified case. Further, an energy calculation is performed which illustrates that an earlier formulation actually results in energy gain for some cases. A more general formula for the constant water surface elevation that corrects this is introduced and tested. It is found that the refined formulation presented here is accurate for hydraulic jumps, steep surge waves, and flood wave propagation in natural channels. The shock capturing capability of the approximate formulation is illustrated for both steady- and unsteady-flow situations using the finite-element method, for which this approximate equation formulation adapts naturally. Using the characteristic-dissipative-Galerkin finite-element scheme, good results are obtained for the case of a hydraulic jump in a diverging rectangular channel, with the maximum percent error associated with the approximate formulation determined to be only 0.34%. For the case of dam break wave propagation in a converging and diverging rectangular channel, the model performs similarly well, with the maximum error only 0.0064%. Further, the approximate formulation is used to simulate the flood routing in a natural channel, the Oldman River in southern Alberta. The computational results are in good agreement with the observed data. The arrival time of peak flow is 5h earlier and the magnitude of peak discharge is only 3.8% lower than the observed value.
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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 | 0.000 | 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".