Limiters for Unstructured Higher-Order Accurate Solutions of the Euler Equations
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Bibliographic record
Abstract
Higher-order finite-volume methods have been shown to be more efficient than second-order methods. However no consensus has been reached on how to eliminating the oscilla-tions caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the application of limiters used for second-order methods to the higher-order case. Requirements for accuracy and efficient convergence are discussed. A new limiting procedure is proposed. Results for the fourth-order accurate solution of transonic and supersonic flows demonstrate good convergence properties and significant qualitative improvement of the solution relative the second-order method. Sub-sonic results demonstrate the superiority of the scheme in smooth flows by the reduction in entropy production. Some aspects of the new limiter can also be successfully applied to reduce the dissipation of second-order schemes with minimal sacrifices in convergence properties. 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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| 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