Nonlinear Frequency-Domain Solver for Vortex Lattice Method
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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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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) | 0.001 | 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 it