On Order Elevation for Unstructured Finite Volume Solvers Using Defect Correction
Bibliographic record
Abstract
Abstract Much of the effort in improving the accuracy of computational fluid dynamics (CFD) simulations is focused on mesh refinement and adaptation although studies have shown that the use of high-order methods are more efficient in improving accuracy. Stability issues, complexity of implementation, and demand of computational resources are some of the key factors hindering the use of high-order methods in commercial CFD solvers. This paper demonstrates an improvement in the order of accuracy of finite volume solutions on unstructured meshes without using a high-order solver. Defect correction and the error transport equation method are the techniques discussed, along with the method for obtaining an appropriate estimate of the truncation error, which is crucial in both these techniques. Methods to obtain high-order interpolation of the control volume averages and high-order integral functionals along curved boundaries are also discussed. Third-order accurate results are obtained for a variety of problems, including the 2D Euler equations, without using a third-order discretization scheme.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| 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".