Application of High-Order Energy Stable Flux Reconstruction Schemes to the Euler Equations
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Bibliographic record
Abstract
The authors recently identified an infinite range of high-order energy stable flux reconstruction (FR) schemes in 1D and on triangular elements in 2D. The new flux reconstruction schemes are linearly stable for all orders of accuracy in a norm of Sobolev type. They are parameterized by a single scalar quantity, which if chosen judiciously leads to the recovery of various well known high-order methods (such as a collocation based nodal discontinuous Galerkin method and a spectral difference method). Identification of such schemes represents a significant advance in terms of understanding why certain FR schemes are stable, whereas others are not. However, to date there have been no studies into how these schemes perform when applied to real world non-linear problems. In this paper, stability and accuracy properties of these new schemes are studied for various two-dimensional inviscid flow problems. The results offer significant insight into the performance of energy stable FR schemes for non-linear problems. It is envisaged the results will aid scheme selection for a given problem, based on its stability and accuracy requirements. I.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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)
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 it