Aerodynamic Shape Optimization for Unsteady Flows: Some Benchmark Problems
Bibliographic record
Abstract
We present an efficient aerodynamic shape optimization framework for optimization problems under unsteady flow conditions. The optimization framework consists of a parallel Newton-Krylov flow solver for multi-block grids and an integrated geometry parameterization and mesh-deformation algorithm based on linear elasticity. We apply the adjoint method to the discretized governing equations to compute the gradients required by the sequential quadratic programming optimization algorithm. We propose two lift constrained drag minimization problems for the purposes of testing and evaluating the framework. First, we consider a laminar flow airfoil optimization problem at a Reynolds number of 800 and also investigate the convexity of the optimization problem. We show that the optimizer is capable of reducing the drag for this problem by about 23% and produces a nearly steady flow compared to the vortex shedding observed for the baseline geometry at the required lift target. The second benchmark case is a lift-constrained drag minimization of an aspect ratio eight rectangular wing in a laminar flow at a Reynolds number of 800. Section shape, twist, and angle of attack are free. Although only partially converged at the time of writing, the preliminary results show a 20% drag reduction.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 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) | 0.001 | 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 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".