Accuracy Assessment of Finite Volume Discretizations of Diffusive Fluxes on Unstructured Meshes
Bibliographic record
Abstract
The results of the 3 rd AIAA Drag Prediction Workshop showed that numerical errors are comparable in magnitude to physical modeling errors. One route to reducing numerical errors is to improve discretization accuracy on a fixed mesh. This paper presents novel techniques for analysis of truncation error for finite-volume discretizations on unstructured meshes. We apply these techniques to compare the truncation error of discretization schemes commonly used for convective flux approximation in cell-centered finite volume solvers. For that purpose, two classes of tests are considered. Analytical tests on topologically regular meshes are done to find the general form of truncation error for both linear and non-linear convection problems. Given the results of the analytic tests, a truncation error metric is defined based on the coefficients associated with the spatial derivatives in the series expansion of the truncation error. More complex numerical tests are conducted to extend the accuracy assessment to general unstructured meshes consisting of both isotropic and anisotropic triangles. We found that the choice of discretization does not change the truncation error of convective fluxes considerably on both isotropic and anisotropic meshes. Also, adding the artificial dissipation term to central discretization does not deteriorate the global accuracy of the flux integral associated with convection problems.
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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 | 0.004 | 0.018 |
| 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".