Tri-quadratic skew upwind scheme for scalar advection in a control-volume-based finite element method
Bibliographic record
Abstract
This paper develops a new tri-quadratic non-inverted skew upwind scheme (NISUS) for additional refinement of nodal integration points in numerical advection–diffusion of scalar transport. Using a control-volume-based finite element method, the performance of the eight-noded hexahedral formulation is compared with tri-quadratic hexahedral elements (27-noded hexahedral). As an extension of the NISUS formulation developed with eight-noded hexahedral elements, the new 27-noded hexahedral version uses isoparametric shape functions and integration point interpolation. The proposed method is applied to three cases of advection–diffusion of heat transfer and energy transport, including radial heat flow in a rotating hollow sphere, advection–diffusion in a cubical cavity, and combined advection/diffusion in an inlet/outlet tank. Performance improvement of the two versions of NISUS in terms of speed, accuracy, and stability are presented as a comparative assessment for the design of energy conversion systems.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".