Bibliographic record
Abstract
Abstract The system of nonlinear shallow‐water equations (SWEs) is a hyperbolic system serving as a primary test problem for numerical methods used in modelling global atmospheric flows. In this article, the SWEs on a rotating sphere are solved on the Yin‐Yang grid by using a domain decomposition method (DDM). This overset grid is singularity free and has a quasi‐uniform grid spacing. It is composed of two identical latitude/longitude orthogonal grid panels that are combined to cover the sphere with partial overlap on their boundaries. On each of the two subgrids, the local solver is based on an implicit and semi‐Lagrangian discretization on a horizontally staggered Arakawa C mesh. The resulting positive definite Helmholtz problem is solved using a Schwarz‐type DDM known as the optimized Schwarz method, which gives better performance than the classical Schwarz method by using specific Robin or higher‐order transmission conditions. Finally, the standard shallow‐water test set is performed in order to show that the DDM solution for SWEs on the Yin‐Yang grid system can reproduce the global solution accurately on the sphere. This work represents a first step in the development of a three‐dimensional forecasting model on the Yin‐Yang grid. © 2011 Crown in the right of Canada. Published by John Wiley & Sons Ltd.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".