Steady three-dimensional turbulent flow computations with a parallel Newton-Krylov-Schur algorithm
Bibliographic record
Abstract
We present computations of steady three-dimensional turbulent flows with a parallel Newton-Krylov-Schur solution algorithm. The algorithm solves the Reynolds-Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model, with the optional use of quadratic constitutive relations. The governing equations are discretized on multi-block structured grids using summation-by-parts operators with simultaneous approximation terms to enforce boundary and block interface conditions. We present a discussion on algorithm performance metrics, including speed, accuracy, and efficiency, and suggest several metrics which can be used for algorithm comparisons, such as convergence time, equivalent right-hand-side evaluations, computing time per grid node, and time required to reach specific functional error levels as compared to grid-converged values. The suggested metrics are applied to the current algorithm in the solution of subsonic and transonic flows around the ONERA M6 and NASA Common Research Model geometries. The results show effective algorithm convergence as grid resolution is increased, converging the residual by 12 orders of magnitude for all cases. A third geometry, based on the 1st AIAA High Lift Prediction Workshop delta wing configuration, provides difficulty in obtaining full convergence, leveling the residual off at a reduction of 4 to 5 orders of magnitude. However, the partially converged solutions show excellent agreement of lift and drag coefficients with experimental data in the angle of attack range of 1 to 40.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 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 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".