Non-oscillatory Lax-Friedrichs Type Central Finite Volume Methods for 3-D Flows on Unstructured Tetrahedral Grids
Bibliographic record
Abstract
We present a 3D finite volume generalization of the l-dimensional Lax-Friedrichs and Nessyahu-Tadmor schemes for hyperbolic equations on unstructured tetrahedral grids. The non-oscillatory central difference scheme of Nessyahu and Tadmor, in which the resolution of the Riemann problem at the cell interfaces is by-passed thanks to the use of the staggered Lax-Friedrichs scheme, is extended here to a two-step, three-dimensional non-oscillatory centered scheme in finite volume formulation. Piecewise linear cell interpolants using Venkatakrishnan’s limiter combined with diverse techniques to estimate the gradients lead to a non-oscillatory spatial resolution of order 2. The fact that the expected second order resolution is not fully attained in 3D for nonlinear systems might be caused by the absence of grid adaptation in our calculations. Numerical results for a linear advection problem with continuous initial conditions in 3D show the accuracy and stability of the method. We also include results for the 3D Euler system (shock tube problem).
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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) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 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 | 0.001 | 0.001 |
| 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".