Hyperbolic conduction: a fast, physical conduction model implemented in smoothed particle hydrodynamics
Bibliographic record
Abstract
ABSTRACT We present the first implementation of hyperbolic thermal conduction in smoothed particle hydrodynamics. Hyperbolic conduction is a physically motivated alternative to traditional, parabolic conduction. It incorporates a relaxation time, which ensures that heat propagates no faster than a physical signal speed. This allows for larger, Courant-like, time-steps for explicit schemes. Numerical solutions of the hyperbolic conduction equations require added dissipation to remain stable at discontinuities and we present a novel scheme for this. Test cases include a simple step, the Sod Shock Tube, the Sedov–Taylor blast, and a super bubble. We demonstrate how longer relaxation times limit conduction, recovering the purely hydrodynamical results, while short relaxation times converge on the parabolic conduction result. We demonstrate that our scheme is stable with explicit Courant-like time-steps and can be orders of magnitude faster than explicit parabolic conduction, depending on the application.
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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 | 0.000 | 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".