Euler flow solution dependency on control volume shape and orientation
Bibliographic record
Abstract
The Behaviour of the numerical solution given by a finite volume method as a function of the shape and orientation of various control volumes is investigated. The study was carried out for the two dimensional Euler equations for inviscid compressible flows solved with Roe's scheme. An object oriented research flow solver (FV+) has been used to handle the construction for a variety of control volume shapes. In particular, cell centered, vertex centered and edge centered control volumes have been studied. The test geometry is a 2-D converging-diverging nozzle which was studied for two different pressure ratios, three types of primary grids each with three types of secondary grids. For each type of primary grid, four levels of refinement have been used. The calculations show significant variations in the solution for different control volume shapes. This affects flow characteristics such as shock location and solution convergence rate. A solution computed with a commercial flow solver is also presented. Work in progress includes extension to 3-D calculation and external flow simulations. Nomenclature U conservative variables H flux vector tti, U2 velocity components nx, ny normal components E specific entalphy M Mach number m number of sides per control volume p density 7 specific heat ratio ft control volume area A£ time step * Research fellow t Professor * Research engineer, NewTech Brake ^ Professor, Associate Fellow ALA A Copyright © 2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. Subscripts L R oo left control volume right control volume free-stream value
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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 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.003 | 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".