Optimal Runge–Kutta schemes for pseudo time-stepping with high-order unstructured methods
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Bibliographic record
Abstract
In this study we generate optimal Runge-Kutta (RK) schemes for converging the Artificial Compressibility Method (ACM) using dual time-stepping with high-order unstructured spatial discretizations. We present optimal RK schemes with between s = 2 and s = 7 stages for Spectral Difference (SD) and Discontinuous Galerkin (DG) discretizations obtained using the Flux Reconstruction (FR) approach with solution polynomial degrees of k = 1 to k = 8. These schemes are optimal in the context of linear advection with predicted speedup factors in excess of 1.80× relative to a classical RK4,4 scheme. Speedup factors of between 1.89× and 2.11× are then observed for incompressible Implicit Large Eddy Simulation (ILES) of turbulent flow over an SD7003 airfoil. Finally, we demonstrate the utility of the schemes for incompressible ILES of a turbulent jet, achieving good agreement with experimental data. The results demonstrate that the optimized RK schemes are suitable for simulating turbulent flows and can achieve significant speedup factors when converging the ACM using dual time-stepping with high-order unstructured spatial discretizations.
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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 | 0.000 | 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