A post-processing technique for stabilizing the discontinuous pressure\n projection operator in marginally-resolved incompressible inviscid flow
Bibliographic record
Abstract
A method for post-processing the velocity after a pressure projection is\ndeveloped that helps to maintain stability in an under-resolved, inviscid,\ndiscontinuous element-based simulation for use in environmental fluid mechanics\nprocess studies. The post-processing method is needed because of spurious\ndivergence growth at element interfaces due to the discontinuous nature of the\ndiscretization used. This spurious divergence eventually leads to a numerical\ninstability. Previous work has shown that a discontinuous element-local\nprojection onto the space of divergence-free basis functions is capable of\nstabilizing the projection method, but the discontinuity inherent in this\ntechnique may lead to instability in under-resolved simulations. By enforcing\ninter-element discontinuity and requiring a divergence-free result in the weak\nsense only, a new post-processing technique is developed that simultaneously\nimproves smoothness and reduces divergence in the pressure-projected velocity\nfield at the same time. When compared against a non-post-processed velocity\nfield, the post-processed velocity field remains stable far longer and exhibits\nbetter smoothness and conservation properties.\n
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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 | 0.000 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".