Application of Gaussian Moment Closure Methods to Three-Dimensional Micro-Scale Flows
Bibliographic record
Abstract
A parallel, block-based, three-dimensional, hexahedral finite-volume scheme with adaptive mesh refinement has been developed for the solution of the 10-moment Gaussian closure for the modelling of fully three-dimensional micro-scale, non-equilibrium flows. The Gaussian closure has been shown to be a more effective tool for modelling rarefied flows lying within the transition regime than the Navier-Stokes equations, which encounter mathematical difficulties approaching free-molecular flows, and is computationally less expensive than particle-based methods for flows approaching the continuum limit. The hyperbolic nature of the moment equations is computationally attractive and the generalized transport equations can be solved in an accurate and efficient manner using Godunov-type finite-volume schemes as considered here. Details are given of the Gaussian closure, along with extensions for diatomic gases and slip-flow boundaries. Numerical results for several canonical flows demonstrate the potential of these moment closures and the parallel solution scheme for accurately predicting fully three-dimensional non-equilibrium flow behaviour.
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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 | 0.001 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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".