A Sharp-Interface Active Penalty Method for the Incompressible\n Navier-Stokes Equations
Bibliographic record
Abstract
The volume penalty method provides a simple, efficient approach for solving\nthe incompressible Navier-Stokes equations in domains with boundaries or in the\npresence of moving objects. Despite the simplicity, the method is typically\nlimited to first order spatial accuracy. We demonstrate that one may achieve\nhigh order accuracy by introducing an active penalty term. One key difference\nfrom other works is that we use a sharp, unregularized mask function. We\ndiscuss how to construct the active penalty term, and provide numerical\nexamples, in dimensions one and two. We demonstrate second and third order\nconvergence for the heat equation, and second order convergence for the\nNavier-Stokes equations. In addition, we show that modifying the penalty term\ndoes not significantly alter the time step restriction from that of the\nconventional penalty method.\n
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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 | 0.000 | 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 | 0.001 | 0.001 |
| 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".