Paired Explicit Runge-Kutta Schemes for Ansys Fluent's Density-Based Solver
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Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2023-2127.vid Recently, a novel time integrator referred to as Paired Explicit Runge-Kutta (P-ERK) schemes, has been proposed for the solution of locally-stiff systems of equations. This approach allows different Runge-Kutta schemes with different numbers of active stages to be assigned based on local stiffness criteria. In this paper, we develop P-ERK schemes for finite volume methods. Then, we verify that P-ERK schemes obtain their designed order of accuracy using an isentropic vortex case. We then evaluate performance of P-ERK schemes in a finite volume solver with benchmark simulations including laminar flow over a circular cylinder, turbulent flow over an SD7003 airfoil, and turbulent flow over a T106A turbine blade cascade. Results demonstrate that P-ERK schemes can significantly accelerate simulations and achieve speed-up factors in excess of four when compared to a standard explicit temporal scheme, while maintaining accuracy with respect to reference data.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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)
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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