Developing a physical influence upwind scheme for pressure‐based cell‐centered finite volume methods
Bibliographic record
Abstract
Summary In the framework of a cell‐centered finite volume method (FVM), the advection scheme plays the most important role in developing FVMs to solve complicated fluid flow problems for a wide range of Reynolds numbers. Advection schemes have been widely developed for FVMs employing pressure‐velocity coupling methodology in the incompressible flow limit. In this regard, the physical influence upwind scheme (PIS) is developed for a cell‐centered finite volume coupled solver (FVCS) using a pressure‐weighted interpolation method for linking the pressure and velocity fields. The well‐known exponential differencing scheme and skew upwind differencing scheme are also deployed in the current FVCS and their numerical results are presented. The accuracy and convergence of the present PIS are evaluated solving flow in a lid‐driven square cavity, a lid‐driven skewed cavity, and over a backward‐facing step (BFS). The flow within the lid‐driven square cavity is numerically solved at Reynolds numbers from 400 to 10 000 on a relatively coarse mesh with respect to other reported solutions. The lid‐driven skewed cavity test case at Reynolds number of 1000 demonstrates the numerical performance of the present PIS on nonorthogonal grids. The flow over a BFS at Reynolds number of 800 is numerically solved to examine capabilities of current FVCS employing the current PIS in inlet‐outlet flow computations. The numerical results obtained by the current PIS are in excellent agreement with those of benchmark solutions of corresponding test cases. Incorporating implicit role of pressure terms in a pressure‐weighted interpolation method and development of PIS provides satisfactory solution convergence alongside the numerical accuracy for the current FVCS. A particular numerical verification is performed for the V velocity calculation within the BFS flow field, which confirms the reliability of present PIS.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".