Advances in Homotopy Continuation Methods in Computational Fluid Dynamics
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Bibliographic record
Abstract
Progress in the development of a homotopy continuation method to globalize the spatiallydiscretized steady flow equations in computational fluid dynamics (CFD) is presented. The algorithm contains many new features developed specifically for application to the large sparse highly parallelized systems encountered in modern CFD. A second-difference dissipation operator common in finite-difference CFD algorithms is used as the homotopy function. Performance is investigated for compressible subsonic and transonic flow over an ONERA M6 wing geometry. Performance of the homotopy algorithm is demonstrated to be comparable to or better than the well-established pseudo-transient continuation method for all inviscid and laminar cases investigated. The algorithm also shows comparable performance to pseudo-transient continuation for turbulent flows (using Reynolds-averaging).
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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 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| 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