A Newton-Krylov solver with a loosely-coupled turbulence model for aerodynamic flows
Bibliographic record
Abstract
Computational solutions of the Navier-Stokes equations have proven to be a useful tool in the design of aircraft. A Newton-Krylov flow solver for unstructured grids is developed in order to demonstrate that a formulation in which the mean-flow and turbulence mechanism equations are loosely coupled can be more economical than a similar fully-coupled formulation. The Favre-averaged Navier-Stokes equations are derived for steady two-dimensional flows, and the turbulence mechanism is described. These equations constitute a model of the physics of aerodynamic flows. The model is validated against experimental data. The objective of this thesis is to examine a means to improve the iterative process by which the solutions are generated. The Newton-Krylov iteration is selected in order to refine the solution, and its features examined. The authors of current Newton-Krylov techniques have fully coupled the turbulence mechanism to the Navier-Stokes equations. A contrast and comparison study made here between the fully-coupled formulation and a loosely-coupled alternative favours the latter. An 'equivalent function evaluation' metric is selected for comparison purposes, and is assessed by means of diverse computers. Published results which use the metric are located, and the present loosely-coupled formulation for unstructured grids is found to be significantly faster in this metric than similar fully-coupled formulations. The advantages of the loosely-coupled formulation with respect to the fully-coupled formulation are stated and future avenues for exploitation of the proposed technology are examined. Appendices consist of: a formalism for the Favre average and consequences of its derivation; a short tract on Taylor series; and an essay on the Frechet differential.
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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 | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| 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".