MPS‐Based Model to Solve One‐Dimensional Shallow Water Equations
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Bibliographic record
Abstract
Abstract Here, a moving particle simulation method is presented to spatially integrate the cross‐sectional average shallow water equations using a prediction‐correction procedure for the time discretization. A density‐ratio equation is derived for the water depth computation according to the particle number density concept. The newly derived equation does not miscalculate the water depth in case an incorrect searching radius parameter is adopted, unlike the typical volume‐summation formula in meshless shallow water flows. A new one‐dimensional Spiky kernel function is developed to satisfy the unity condition employed in the Newton‐Raphson iteration to calculate the water depth. Dynamic stabilization is adopted to capture shockwave problems, a case‐independent technique based on the inelastic collision with unequal masses. The convective flux term is eliminated under the Lagrangian framework, and so the momentum is adequately conserved without the need for any special treatment. The proposed scheme maintains the exact C‐property, meaning that the water depth gradient and bed slope are hydrostatically well balanced within a discretized solution domain. Compared to analytical solutions and experimental data, the results of this study reveal that the present model is a robust numerical solver without unphysical oscillations. It can capture various shock problems, including steep gradient shock‐front, discontinuous wet bed, transcritical flow regimes, and irregular bed topography. The present model can also simulate the dry‐wet flow transition influenced by friction without experiencing any divisions by zero, negative values, or unphysical perturbations. This advantage is basically due to the water particles' absence and presence for the dry and wet regions, respectively.
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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 | 0.000 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
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