A stabilized finite element method based on characteristic‐based polynomial pressure projection scheme for incompressible flows
Bibliographic record
Abstract
Abstract In this paper, a characteristic‐based polynomial pressure projection (CBP3) scheme is proposed to stabilize finite element method for solving incompressible laminar flow. The characteristic‐Galerkin (CG) method is adopted as the stabilization for convection caused oscillation in CBP3 scheme. The pressure oscillation caused by incompressible constraint is stabilized by the polynomial pressure projection (P3) technique. Proposed scheme is suitable for any element using the equal‐order approximation for velocity and pressure. In this paper, the linear triangular and bilinear quadrilateral elements are adopted. The constant pressure projection is used for triangular elements. The CBP3 formulations for quadrilateral element are derived using both constant and linear pressure projections. Besides, the quasi‐implicit second‐order time stepping is adopted. The verification of CBP3 scheme implementation and validation of CBP3 scheme are accomplished by calculating several benchmarks. The results of CBP3 scheme reveal that the linear pressure projection for quadrilateral element is not appropriate due to its severe pressure oscillation. The well‐agreed results of CBP3 scheme using constant pressure projection demonstrate its good stabilization for FEM to solve both low and relatively high Reynolds number flows.
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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 | 0.001 |
| 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 | 0.001 | 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".