On Order Elevation for Unstructured Finite Volume Solvers Using Defect Correction
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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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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 | 0.001 |
| 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)
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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