Obtaining and Verifying High-Order Unstructured Finite Volume Solutions to the Euler Equations
Bibliographic record
Abstract
Interest in high-order unstructured-mesh finite volume methods continues to grow, as researchers are attracted both to the possibilities of high-accuracy solutions on coarse meshes and to applications for which high-order accuracy is all but mandatory, including large-eddy simulations for complex geometries. A major obstacle for those interested in developing a high-order solver, however, is that there are many more details that must be exactly right for a nominally-high-order scheme to be genuinely-high-order than for a second-order scheme to be second-order. In many cases, these details are either omitted or glossed over in the literature. This paper attempts to close this gap by illuminating a number of obscure, or often overlooked, aspects of correctly implementing a high-order-accurate unstructured-mesh finite volume solver. We discuss reconstruction, flux integration, curved-boundary treatment, and demonstrating order of accuracy. In each case, we describe test cases that are appropriate for confirming the correct behavior of a high-order code, as well as demonstrating some of the common pitfalls in implementation and showing their effects. We hope that this paper will serve other researchers as a practical guide to creating their own high-order-accurate solvers.
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 | 0.006 | 0.044 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".