A direction splitting scheme for Navier–Stokes–Boussinesq system in spherical shell geometries
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Bibliographic record
Abstract
Abstract This article introduces a second‐order direction splitting method for solving the incompressible Navier–Stokes–Boussinesq system in a spherical shell region. The equations are solved on overset Yin–Yang grids, combined with spherical coordinate transforms. This approach allows to avoid the singularities at the poles and keeps the grid size relatively uniform. The downside is that the spherical shell is subdivided into two equally sized, overlapping subdomains that requires the use of Schwarz‐type iterations. The temporal second‐order accuracy is achieved via an artificial compressibility scheme with bootstrapping. The spatial discretization is based on second‐order finite differences on the Marker‐And‐Cell stencil. The entire scheme is implemented in parallel using a domain decomposition iteration and a direction splitting approach for the local solves. The stability, accuracy, and weak scalability of the method is verified on a manufactured solution of the Navier–Stokes–Boussinesq system while its practicality is demonstrated on the natural convection problem in the gap between two concentric spheres.
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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 | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
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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