Fully Discrete Entropy-Stable Flux Reconstruction Scheme for Compressible Flows through the Relaxation Runge-Kutta Method
Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2023-0663.vid Entropy-stable methods are able to improve stability and accuracy of high-fidelity flow simulations in aerodynamics problems by adding the minimum amount of dissipation for nonlinear stability. Discontinuous Galerkin and flux reconstruction methods have been used in split forms to achieve semi-discrete entropy stability. We use the relaxation Runge-Kutta (RRK) method in conjunction with a split-form flux reconstruction scheme to construct a robust, fully-discrete entropy conserving scheme. The fully-discrete scheme ensures stability properties are retained when using relatively large timestep size, while adding only an algebraic equation. We demonstrate the properties of the fully-discrete scheme using entropy-conservative problems with the Burgers' and Euler equations. The fully-discrete entropy-conserving scheme is able to conserve entropy to machine precision in all test cases, while maintaining the expected orders of convergence of the semi-discrete scheme. We hope to apply the entropy-stable scheme presented in this conference proceeding to viscous, industrially-relevant cases, and thoroughly explore an entropy-stable version of the fully-discrete scheme.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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) | 0.003 | 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".