Unstructured High-Order Accurate Finite-Volume Solutions of the Navier-Stokes Equations
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Bibliographic record
Abstract
A nite-volume scheme utilizing a fourth-order reconstruction for convective and di usive uxes of the Navier-Stokes equations is presented. The reconstruction is obtained e ciently by precomputing the pseudo-inverse of the reconstruction matrix. Viscous boundary conditions are handled by introducing additional rows in the reconstruction matrices. Rapid convergence of steady-state problems is made possible by computing the exact ux Jacobian and the use of a Newton-GMRES algorithm. A grid convergence study of cylindrical Couette ow is used to demonstrate the order of accuracy of the scheme. Laminar ow over an airfoil on a sequence of anisotropic grids is also used to qualitatively demonstrate the superior accuracy of the fourth-order scheme.
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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 | 0.001 |
| Science and technology studies | 0.002 | 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