Drag Minimization Based on the Navier–Stokes Equations Using a Newton–Krylov Approach
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Bibliographic record
Abstract
A methodology is presented for performing numerical aerodynamic shape optimization based on the three-dimensional Reynolds-averaged Navier–Stokes (RANS) equations. An initial multiblock structured mesh is first fit with B-spline volumes that form the basis for a hybrid mesh movement scheme that is tightly integrated with the geometry parameterization based on B-spline surfaces. The RANS equations and the one-equation Spalart–Allmaras turbulence model are solved in a fully coupled manner using an efficient parallel Newton–Krylov algorithm with approximate-Schur preconditioning. Gradient evaluations are performed using the discrete-adjoint approach with analytical differentiation of the discrete flow and mesh movement equations. The overall methodology remains robust even in the presence of large shape changes. Several examples of lift-constrained drag minimization are provided, including a study of the common research model wing geometry, a wing–body–tail geometry with a prescribed spanwise load distribution, and a blended-wing–body configuration. An example is provided that demonstrates that a wing optimized based on the Euler equations exhibits substantially inferior performance when subsequently analyzed based on the RANS equations relative to a wing optimized based on the RANS equations.
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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