Verification of a Free Surface Adaptive Finite Element Solution Algorithm
Bibliographic record
Abstract
This paper presents a verification of an adaptive finite element algorithm for the computation of free surface flows. We use an arbitrary Lagrangian Eulerian description for the computation of the free surface. Hence, the mesh follows the deformations of the free surface. A pseudo-solid approach is used to compute the mesh deformations. Special attention must be payed to the variational formulation of the Navier-Stokes equations and to the computation of the mesh velocity to satisfy the Geometric Conservation Law (GCL). The GCL ensures that the fixed mesh order of accuracy of the time integrator is preserved on moving meshes. Thus a 3 rd order accurate implicit Runge Kutta scheme has been used. The implementation of the free surface boundary condition is then verified with the method of the manufactured solution. The solution is computed with an adaptive finite element code. An analytical solution of the free surface and Navier-Stokes equations is developed. It is used as a reference to verify the spatial and temporal convergence rates of the method. Other test cases are also presented.
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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 | 0.001 | 0.008 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".