Hybrid Navier–Stokes–Direct Simulation Monte Carlo Automatic Mesh Optimization for Hypersonics
Bibliographic record
Abstract
This paper describes the development of an unstructured hybrid finite element Navier–Stokes (NS)–direct simulation Monte Carlo (DSMC) framework for hypersonic flows. State-based coupling is employed and simulations of varying thermochemical complexity demonstrate the accuracy, robustness, and computational efficiency of the hybrid all-Mach algorithm. An automatic mesh optimization process using a posteriori error estimates based on the Hessian of the solution goes much further than traditional mesh adaptation processes by equidistributing the error estimator and producing a “single optimal hybrid mesh” with no increase in mesh size and with much higher accuracy. The DSMC region cells of the resulting optimal mesh are smaller than in NS regions and are sized to the local mean free path. Mesh optimization is also shown to greatly improve the quality of the hybrid interfaces from those of the initial mesh. Unstructured meshes are found to represent the hybrid interfaces smoothly, while structured meshes showcase a castellated pattern in the interfaces. The optimal hybrid meshes are found to be statistically similar to optimal full DSMC meshes, thus highlighting the solver independence of the optimizer. Such a coupled hybrid mesh optimization strategy can therefore tackle hypersonic flows with multiscale flow features at any degree of rarefaction.
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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".