Entropy Stable Split Forms for the Flux Reconstruction High-Order Method: Numerical Validation
Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2021-1444.vid The flux reconstruction method has gained popularity in the research community as it recovers promising high-order methods through modally filtered correction fields, such as the Discontinuous Galerkin (DG) method, on unstructured grids over complex geometries. The attraction of the method follows with its stability proofs for the linear advection problem on linear elements, under a class of energy stable flux reconstruction (ESFR) schemes also known as Vincent-Castonguay-Jameson-Huynh (VCJH) schemes. Additionally, split forms have gained popularity in the research community due to the proofs of robustness for nonlinear, unsteady problems on unstructured grids, albeit only having been proved for the strong form DG scheme and numerically shown for the collocated strong form ESFR scheme for the Euler equations. This paper follows a new approach for implementing ESFR schemes on nonlinear split forms, which recovers the classical ESFR scheme on linear problems. The new ESFR approach is proven to not change the order of accuracy, and allows for proofs of stability for both the ESFR strong and weak forms, on unstructured and curvilinear grids. The methodology is demonstrated for Burgers' equation with numerical results demonstrating stability for all ESFR schemes.
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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 | 0.002 | 0.006 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.007 | 0.002 |
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".