An adaptive central-upwind scheme on quadtree grids for variable density\n shallow water equations
Bibliographic record
Abstract
Minimizing computational cost is one of the major challenges in the modelling\nand numerical analysis of hydrodynamics, and one of the ways to achieve this is\nby the use of quadtree grids. In this paper, we present an adaptive scheme on\nquadtree grids for variable density shallow water equations. A scheme for the\ncoupled system is developed based on the well-balanced positivity-preserving\ncentral-upwind scheme proposed in [18]. The scheme is capable of exactly\npreserving "lake-at-rest" steady states. A continuous piecewise bi-linear\ninterpolation of the bottom topography function is used to achieve higher-order\nin space in order to preserve the positivity of water depth for the point\nvalues of each computational cell. Necessary conditions are checked to be able\nto preserve the positivity of water depth and density, and to ensure the\nachievement of a stable numerical scheme. At each timestep, local gradients are\nexamined to find new seeding points to locally refine/coarsen the computational\ngrid.\n
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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 | 0.001 | 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".