An adaptive central‐upwind scheme on quadtree grids for variable density shallow water equations
Bibliographic record
Abstract
Abstract Minimizing computational cost is one of the major challenges in the modeling and numerical analysis of hydrodynamics, and one of the ways to achieve this is by the use of quadtree grids. In this article, we present an adaptive scheme on quadtree grids for variable density shallow water equations. A scheme for the coupled system is developed based on the work of [M.A. Ghazizadeh, A. Mohammadian, and A. Kurganov, Computers & Fluids , 208 (2020)]. The scheme is capable of exactly preserving “lake‐at‐rest” steady states. A continuous piecewise bi‐linear interpolation of the bottom topography function is used to achieve higher‐order in space in order to preserve the positivity of water depth for the point values of each computational cell. Necessary conditions are checked to be able to preserve the positivity of water depth and density, and to ensure the achievement of a stable numerical scheme. At each timestep, local gradients are examined to find new seeding points to locally refine/coarsen the computational grid.
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How this classification was reachedexpand
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".