Numerical Prediction of Three-Dimensional Non-Equilibrium Gaseous Flows Using the Gaussian Moment Closure
Bibliographic record
Abstract
A parallel, implicit, adaptive mesh re nement (AMR), upwind, nite-volume scheme is described for the solution of the 10-moment Gaussian closure and the combined hyperbolic modelling treatment / numerical method is applied to the prediction of three-dimensional, non-equilibrium, micro-scale, gaseous ows. The Gaussian moment equations are based on a maximum-entropy closure applied to the Boltzmann equation and provides a fullyrealisable and strictly hyperbolic description of non-equilibrium gaseous ows that is valid from the near-equilibrium or continuum limit, through the transition regime, up to the near-collisionless or free-molecular ow limit. Although this somewhat simpli ed mathematical model does not incorporate the e ects of heat transfer, it has been shown to accurately describe non-equilibrium momentum transport for a range of micro-scale ows and is very representative of other higher-order closures that would potentially include the e ects of non-equilibrium thermal transport. The hyperbolic moment equations are readily amenable to solutions using a Godunov-type, upwind, nite-volume scheme on an AMR mesh. The proposed upwind scheme makes use of Riemann-solver-based ux functions and limited linear reconstruction to provide accurate and monotonic solutions, even in the presence of large solution gradients and/or under-resolved solution content on threedimensional, multi-block, bodytted, hexahedral mesh. A block-based AMR strategy is adopted herein to allow for local re nement of the computational mesh. A rather e ective and scalable parallel implicit time-marching scheme based on a Jacobian-free inexact Newton-Krylov-Schwarz (NKS) approach with additive Schwarz preconditioning and domain partitioning following from the multi-block AMR mesh is used for the solution of the non-linear ordinary-di erential equations that result from the application of the upwind spatial discretisation procedure. Details are given of the Gaussian closure, along with suitable extensions for diatomic gases and slipow boundaries, and the proposed nite-volume method. Numerical results for several canonical ow problems demonstrate the potential of hyperbolic moment closures, combined with an e cient parallel solution method, for accurately predicting fully three-dimensional non-equilibrium gaseous ow behaviour.
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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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".