p-adaptive hybridized flux reconstruction schemes
Bibliographic record
Abstract
This paper presents p-adaptive hybridized flux reconstruction schemes to reduce the computational cost of implicit discretizations. We first introduce spatial and temporal discretization and discuss the adaptation algorithm via a nondimensional vorticity indicator for hybridized methods with globally continuous and globally discontinuous numerical traces. At each adaptation level, projection operations are applied to determine the new space based on the element-wise projected solution and transmission conditions. We validate our implementation and analyze performance via numerical examples. Specifically, we show via an isentropic vortex that p-adaptive hybridization of both HFR and EFR methods results in comparable numerical error to standard p-adaptive and p-uniform FR discretizations with a fraction of degrees of freedom. 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 against p-uniform FR discretizations. Similarly, results for a NACA 0012 airfoil at Re=10,000 demonstrate speedup factors close to 6 against p-adaptive FR discretizations and up to 33 against p-uniform conventional FR. Hence, combining hybridization with adaptation yields a significant reduction in computational cost compared with standard 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".