Adjoint Error Correction on Unstructured Finite Volume Solvers
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Bibliographic record
Abstract
Abstract One of the major applications of the adjoint method is the improvement in the order of accuracy of integral quantities obtained from CFD simulations. Although the theory requires the use of a smooth interpolation of the solution, this has seldom been used with unstructured finite volume solvers. In this paper, the adjoint based correction is applied to output functionals obtained using finite volume method on unstructured meshes. A smoothing spline based on a C1 continuous representation of the discrete solution is employed to reduce the random noise in the solution and to improve the rate of convergence of the derivatives. Tests performed on randomly perturbed meshes in 1-D showed fourth-order convergence of output functionals obtained from second-order solution, corrected using the truncation error obtained using the smoothing spline and second-order accurate adjoint solution. The extension of this method to 2-D problems showed superconvergence for output functionals and improvements over existing results.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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