Mesh and polynomial adaptation for high-order discretizations of compressible flows
Bibliographic record
Abstract
The aerospace research and industry sectors are relying increasingly on numerical simulations to gain insight into aerodynamic flows. However, the complexity of these flows and the broad range of scales they exhibit still represent a serious challenge to the current generation of computational methods. This thesis presents developments to high-order accurate (> 2nd order) schemes aimed at addressing these limitations. The topic is tackled from the perspectives of enhanced resolution and adaptive error-control. Firstly, an extension of the Lifting-Collocation-Penalty (LCP) scheme to spatially-varying polynomial approximations is presented. This formulation is used to perform efficient polynomial-adaptive computations of compressible flows. The focus is put on the adequate inter-cell flux transfer, and stability analysis of the resulting scheme. Secondly, improved error-control via adjoint-driven mesh refinement is demonstrated. The connection between the global error-norm and the truncation error is established through an adjoint problem. This link provides valuable information about error-propagation patterns, and is shown to be useful for adaptive mesh refinement.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 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".