On the Invalidity of the Extended Navier-Stokes Equations to Compute Rarefied Gas Flows in a Cylinder Array
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Bibliographic record
Abstract
Computing rarefied gas flow fields through porous media with the Boltzmann equation is computationally prohibitive for industrial use. To reduce computational cost, extensions of the Navier-Stokes equations with phenomenological slip boundary conditions have been proposed. Models relying on a hypothesis of proportionality between the effective mean free path and the effective viscosity were previously validated for unidimensional planar and concentric geometries, but lacked verification for intermediate complexity cases like a bidimensional flow through a cylinder array. This article proposes using a lattice Boltzmann method, with the effective mean free path calculated via a verified ray-tracing algorithm. Although excellent agreement with experimental data was found for slit flow, quantitative agreement was not achieved for flow through a cylinder array, despite model convergence at a sublinear order (∼0.52). The study discusses the limitations of the extended Navier-Stokes model, concluding that it is unsuitable for rarefied gas flows with transverse components.
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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 | 0.001 | 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 | 0.001 | 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 it