Applications of the Unsteady Error Transport Equation on Unstructured Meshes
Bibliographic record
Abstract
A numerical study of using the error transport equation, an auxiliary problem to a set of model equations, is performed to obtain higher-order accurate error estimates and corrections for applications in unsteady compressible flow. In many such applications, a functional of the solution is often examined as a proxy for the accuracy of the solution itself. Several measures of time-dependent functionals are used for test cases that have a periodic steady-state solution. The approach is verified by examining unsteady functionals for diffusion and advection model problems, and then the error transport method is applied to the von Kármán vortex shedding test case, a difficult problem to establish accuracy properties on its own. It was found that scalar measures of the unsteady functionals not only give the order of accuracy that would be expected from a primal discretization only but also the expected higher-order accuracy if the functionals were computed using the solutions corrected by this accurate error estimate, all without the otherwise necessary requirement of discretizing to higher order in both time and space for the primal problem. The results are consistent with previous studies on solution error using simple test cases with manufactured solutions.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| 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".