An Eulerian Approach with Mesh Adaptation for Highly Accurate 3D Droplet Dynamics Simulations
Bibliographic record
Abstract
Two main approaches are available when studying droplet dynamics for in-flight icing simulations: the Lagrangian approach, in which each droplet trajectory is integrated until it impacts the vehicle under study or when it leaves it behind without impact, and the Eulerian approach, where the droplet dynamics is solved as a continuum. In both cases, the same momentum equations are solved. Each approach has its advantages. In 2D, the Lagrangian approach is easy to code and it is very efficient, particularly when used in combination with a panel method flow solver. However, it is a far less practical approach for 3D simulations, particularly on complex geometries, as it is not an easy task to accurately determine the droplet seeding region without a great number of droplet trajectories, dramatically increasing the computing cost. Converting the impact locations into a water collection distribution is also a complex task, since droplet trajectories in 3D can follow convoluted paths. One of the advantages of the Lagrangian approach is the crisp definition of the shadow zone as it is clearly defined by the first trajectory to graze the surface of the vehicle. The Eulerian approach is much simpler to use with complex geometries, solving the entire domain as a whole, using the same grid as for the airflow, and there is no need to seed trajectories. For this reason, it is the preferred approach in most 3D icing solvers. One of its disadvantages, however, is that discontinuities, such as shadow zone limits or impingement limits, are usually not very sharply defined, with smoothing due to numerical dissipation and the grid, optimized heuristically for the airflow calculation, not being sufficiently fine in regions of solution discontinuities in the droplet solution. This paper presents a refined approach in the use of Eulerian algorithms for icing simulations by introducing a mesh adaption process simultaneously based on the airflow solution and the droplet solution. The results show the great potential of this approach in capturing the solution discontinuities very sharply, significantly reducing the uncertainty in determining shadow zone heights and impingement limits.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".