A finite volume method to solve the Navier-Stokes equations for incompressible flows on unstructured meshes
Bibliographic record
Abstract
A method to solve the Navier--Stokes equations for incompressible viscous flows and the convection and di#usion of a scalar is proposed in the present paper. This method is based upon a fractional time step scheme and the finite volume method on unstructured meshes. A recently proposed di#usion scheme with interesting theoretical and numerical properties is tested and integrated into the Navier--Stokes solver. Predictions of Poiseuille flows, backward-facing step flows and lid-driven cavity flows are then performed to validate the method. We finally demonstrate the versatility of the method by predicting buoyancy force driven flows of a Boussinesq fluid (natural convection of air in a square cavity with Rayleigh numbers of 10 ). 2000 ditions scientifiques et mdicales Elsevier SAS Navier--Stokes / finite volume method / unstructured mesh / fractional time step / di#usion scheme / lid-driven cavity flow / Boussinesq fluid / natural convection / buoyancy force Rsum --- Une mthode des volumes finis pour la rsolution des quations de Navier--Stokes pour des coulements incompressibles maillages non structurs. Cet article propose une mthode de rsolution des quations de Navier--Stokes pour les coulements visqueux incompressibles et la convection et di#usion d'un scalaire. Celle-ci est base sur un schma pas de temps fractionnaire et la mthode des volumes finis sur maillages non structurs. Un schma pour la di#usion, propos rcemment, dont les proprits thoriques et numriques sont intressantes, est test puis intgr dans un solveur des quations de Navier--Stokes. Des simulations d'coulement de Poiseuille, de marche descendante et de cavit carre entrane, ont permis de valider la mthode. Enfin, la polyvalence de la mthode est illustre par des simulations d'coulement d'un fluide d...
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| 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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".