Free-surface Flow Lagrangian Sensitivities
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Bibliographic record
Abstract
A Continuous Lagrangian Sensitivity Equation Method is presented for free-surface ows. Using a front-tracking approach, the free-surface matches one of the boundaries of the computational domain and follows its deformations in time while grid motions are accounted for by an Arbitrary Lagrangian Eulerian approach. The Lagrangian sensitivity equations are derived formally by implicit total (material) di erentiation of the ow equations for shape parameters. A mapping must be used to relate the undeformed and deformed con gurations. To provide a general framework to generate this mapping for unstructured meshes and complex geometries, we use pseudo-elasticity equations. The sensitivity of free-surface boundary conditions are presented in details. Code Veri cation is performed by the Method of Manufactured Solution for the ow and their Lagrangian sensitivities. On the application side, we present the sensitivity of the location of an underwater cylinder on loads and free surface location interacting with generated swell.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 it