Three-Dimensional Aerodynamic Computations on Unstructured Grids Using a Newton-Krylov Approach
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Bibliographic record
Abstract
Abstract A Newton–Krylov algorithm is presented for the compressible Navier–Stokes equations in three dimensions on unstructured grids. The algorithm uses a preconditioned matrix-free Krylov method to solve the linear system that arises in the Newton iterations. Incomplete factorization is used as the preconditioner, based on an approximate Jacobian matrix after the reverse Cuthill–McKee reordering of the unknowns. Several approximate viscous operators that involve only the nearest neighboring terms are studied to reduce the cost of preconditioning. The performance of the algorithm is demonstrated through numerical studies of the ONERA M6 wing and the DLR-F6 wing-body configuration. A ten-order-of-magnitude residual reduction for the wing and wing-body configurations can be obtained with a computing cost equivalent to 5500 and 8000 function evaluations, respectively, on grids with a half million nodes.
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 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