Hybridization of a polynomial adaptive high-order solver for unsteadycompressible flows
Bibliographic record
Abstract
We present p-adaptive hybridized flux reconstruction schemes to reduce the computational cost of implicit discretizations using a nondimensional vorticity indicator.At each adaptation level, we apply a projection operation to the new space based on the element-wise projected solution and the transmission conditions.We validate our implementation and analyze performance via numerical examples.Specifically, we show that p-adaptation of hybridizable flux reconstruction (HFR) methods results in comparable numerical error to standard p-adaptive and p-uniform standard flux reconstruction (FR) discretizations with a fraction of degrees of freedom.Performance results for a cylinder at Re = 150 showcase speedup factors in excess of 6 for hybridized methods in comparison with p-adaptive standard FR schemes, and up to 40 compared to p-uniform FR discretizations.Similarly, results for a NACA 0012 airfoil at Re = 10, 000 demonstrate speedup factors close to 6 compared to p-adaptive FR discretizations, and up to 33 compared to p-uniform conventional FR.Hence, combinining hybridization with adaptation yields a significant reduction in computatonal cost compared to conventional implicit discretizations.
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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 | 0.000 | 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".