Verification of a Free Surface Adaptive Finite Element Solution Algorithm
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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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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 | 0.001 | 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) | 0.000 | 0.000 |
Machine scores (provisional)
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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