Nonlinear Frequency-Domain Solver for Vortex Lattice Method
Bibliographic record
Abstract
This Paper presents a nonlinear frequency-domain solver for the vortex lattice method. Assuming a periodic solution, the wing circulation is represented in time by a Fourier series without the assumption of small-amplitude oscillations and with a prescribed wake. The linear system of the vortex lattice method is developed in the frequency domain, allowing the periodic solution to be formulated as a steady problem. Two different approaches are proposed to solve the nonlinear system of equations, an iterative segregated approach and a direct frequency-domain approach. The method is verified against two-dimensional Theordorsen theory as well as three-dimensional solutions from the doublet lattice method and the time-domain unsteady vortex lattice method. The spectral accuracy of the method is demonstrated as is its capabilities of capturing nonlinear effects from wake intersections. The resulting time-spectral vortex lattice method solver is computationally efficient with precision comparable to the time-domain unsteady vortex lattice method solver, thus making the approach interesting for aerospace applications.
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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 | 0.000 | 0.002 |
| 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 | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 0.003 |
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".