Equivalent Rate Constant for Numerical Simulation of Linear Convection-Diffusion-Reaction
Bibliographic record
Abstract
Abstract The accurate numerical modelling of reactive flow is essential for the interpretation of experimental measurements and the design of field-scale processes. Sharp reaction fronts are difficult to capture using traditional numerical schemes, unless fine grid numerical simulations are used; however, fine grid simulations are computationally expensive. On the other hand, using coarse grid block simulations leads to excessive front dissipation and inaccurate results. In most practical cases, it is not feasible to choose small grid blocks; therefore, one needs to account for the small-scale gradients that cannot be captured by coarse grid blocks when using traditional methods. As a first step toward the development of upscaling techniques for reaction kinetics, an equivalent reaction constant for a simple steady-state convection-diffusion-reaction (CDR) was determined. This shows how an effective reaction constant can be obtained as a function of the Peclet number, Thiele modulus and size of the reaction zone, such that the coarse grid simulation agrees with the fine grid simulation.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".