Gas Micro-Flow Modelling Based on Regularized 13-Moment-Equations
Bibliographic record
Abstract
We summarize our recent contributions to the development of macroscopic transport equations for gas micro-flows. A combination of the Chapman-Enskog expansion and Grad’s moment method in kinetic theory of gases yields the Regularized 13-Moment-Equations (R13 equations). These equations overcome deficiencies of Grad’s equations or Burnett models. They are asymptotically of super-Burnett order, i.e., of third order in the Knudsen number and linearly stable for all wave frequencies. In addition, a complete set of boundary conditions can derived from the accommodation boundary conditions of the Boltzmann equations. Mathematically, more boundary conditions are required and they can be derived from the R13 system itself through coherence relations. We present micro-channel and shock wave simulations to prove that R13 is a reliable and efficient continuum model for micro-flows of gases with moderate Knudsen numbers.
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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 | 0.000 |
| 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".