Adjoint Error Correction on Unstructured Finite Volume Solvers
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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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 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".