A Comparison of Higher-Order Methods on a Set of Canonical Aerodynamics Applications
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Bibliographic record
Abstract
Higher-order discretizations have the potential to reduce the computational cost required to achieve a desired error level. In this study, we consider higher-order discretizations of the conservation equations suitable for unstructured, triangular grids. In particular, the methods studied include continuous (SUPG/GLS) and classical discontinuous Galerkin (DG) finite element methods, the correction procedure via reconstruction (CPR) formulations of the DG and spectral volume methods, and cell and vertex-centered finite volume (FV) algorithms. This paper presents subsonic and supersonic, inviscid results for a canonical set of aerodynamic applications. Error convergence and computational performance of these discretizations are compared, and preliminary results indicate that the methods perform relatively similarly. When singularities are present in the flow solutions and uniformly refined meshes are used, all methods fail to achieve optimal convergence rates, and the performance benefits of the higher-order discretizations are reduced; adaptive meshing improves the efficiency of the higher-order method and recovers optimal convergence rates.
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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) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it