Interface and Boundary Schemes for High-Order Methods
Bibliographic record
Abstract
High-order finite-difference methods show promise for delivering efficiency improve-ments in some applications of computational fluid dynamics. Their accuracy and efficiency are dependent on the treatment of boundaries and interfaces. Interface schemes that do not involve halo nodes offer several advantages. In particular, they are an effective means of dealing with mesh nonsmoothness, which can arise from the geometry definition or mesh topology. In this paper, two such interface schemes are compared for a hyperbolic prob-lem. Both schemes are stable and provide the required order of accuracy to preserve the desired global order. The first uses standard difference operators up to third-order global accuracy and special near-boundary operators to preserve stability for fifth-order global accuracy. The second scheme combines summation-by-parts operators with simultaneous approximation terms at interfaces and boundaries. The results demonstrate the effective-ness of both approaches in achieving their prescribed orders of accuracy and quantify the error associated with the introduction of interfaces. Overall, these schemes offer several advantages, and the error introduced at mesh interfaces is small. Hence they provide a highly competitive option for dealing with mesh interfaces and boundary conditions in high-order multiblock solvers, with the summation-by-parts approach with simultaneous approximation terms preferred for its more rigorous stability properties. I.
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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".