Restoring the missing vorticity in advection-projection fluid solvers
Bibliographic record
Abstract
Most visual effects fluid solvers use a time-splitting approach where velocity is first advected in the flow, then projected to be incompressible with pressure. Even if a highly accurate advection scheme is used, the self-advection step typically transfers some kinetic energy from divergence-free modes into divergent modes, which are then projected out by pressure, losing energy noticeably for large time steps. Instead of taking smaller time steps or using significantly more complex time integration, we propose a new scheme called IVOCK (Integrated Vorticity of Convective Kinematics) which cheaply captures much of what is lost in self-advection by identifying it as a violation of the vorticity equation. We measure vorticity on the grid before and after advection, taking into account vortex stretching, and use a cheap multigrid V-cycle approximation to a vector potential whose curl will correct the vorticity error. IVOCK works independently of the advection scheme (we present examples with various semi-Lagrangian methods and FLIP), works independently of how boundary conditions are applied (it just corrects error in advection, leaving pressure etc. to take care of boundaries and other forces), and other solver parameters (we provide smoke, fire, and water examples). For 10 ~ 25% extra computation time per step much larger steps can be used, while producing detailed vorticial structures and convincing turbulence that are lost without correction.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".