A Newton’s solver for high-order wall distance computation on three-dimensional curved, unstructured meshes
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Bibliographic record
Abstract
Accurate wall distance computation is essential in high-order turbulent flow simulations involving complex geometries. This paper presents a new higher-order approach to compute wall distance on three-dimensional, curved, unstructured meshes. The method uses Lagrange interpolation polynomials representing the mesh to formulate an optimization problem whose solution yields the wall distance. The domain is swept from the wall boundaries inward, and the optimization problem is solved for every vertex using Newton’s method. The algorithm is modified for domains with sharp edges, wall corners, or multiple wall boundaries. In problems with non-curved wall boundaries, the method finds the exact wall distance. For curved wall boundaries, when using cubic Lagrange polynomials for the mesh, the method achieves O ( h 4 ) accuracy for the wall distance and O ( h 3 ) accuracy for the normal-to-wall vector. Increasing the accuracy of the Lagrange functions used to define the mesh further improves the method’s order of accuracy. • Introduced a new higher-order wall distance computation method for 3-D curved grids. • Used Lagrange interpolation polynomials to formulate an optimization problem. • Achieved O ( h 4 ) accuracy for wall distance and O ( h 3 ) accuracy for normal vectors. • Adapted the method for cases with sharp edges and multiple wall boundaries. • Demonstrated fast convergence times, suitable for parallel processing.
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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 it