Streamline Tracing Methods Based on Piecewise Polynomial Pressure Approximations
Bibliographic record
Abstract
Abstract In this paper, a unified approach for developing streamline tracing method is proposed based on piecewise polynomial pressure approximation functions. It is designed for the numerical schemes that solve the pressure solution at grid blocks while the interior velocity field remains unknown. The suitable velocity approximation functions are derived through analytical differentiation of pressure functions. They better represent the relationship between velocity field and pressure distribution in reality, satisfy the Laplace equation everywhere in a grid block, and ensure local mass conservation and normal flux continuity. Based on different polynomial pressure functions, the Trilinear/Bilinear and Cubic streamline tracing methods are developed. Additionally, a piecewise parabolic velocity reconstruction method is proposed to extend the application of the Cubic method to first‐order numerical schemes. The accuracy and efficiency of the newly proposed methods are evaluated through comparing it with the Pollock and the high‐order method in terms of velocity approximations and computational cost in numerical cases. Comparison results indicate that the Cubic method delivers the most accurate results at the same computational cost.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| 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 | 0.001 |
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".