Gradient-based polynomial adaptation indicators for high-order methods
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Bibliographic record
Abstract
This work introduces two new non-dimensional gradient-based adaptation indicators for feature-based polynomial adaptation with high-order unstructured methods when used for turbulent flows. Recently, the Flux Reconstruction (FR) approach has been introduced as a unifying framework for high-order unstructured spatial discretizations. To achieve high-order accuracy, FR utilizes an element-wise polynomial representation of the solution. In the current work, we consider three indicators for local adaptation of this polynomial degree. One, introduced previously, uses a non-dimensional maximal vorticity norm. Two new indicators are then introduced using the Frobenius norm of the velocity gradient, and the eigenvalue modulus of the velocity gradient, both normalized by the maximum local grid spacing and free stream velocity. These feature-based methods are simple to implement and have the potential to track small-scale turbulent structures that arise in scale-resolving simulations, such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES). The vorticity, gradient, and eigenvalue-based polynomial adaptation strategies with the FR approach are used to solve the compressible Navier–Stokes equations. DNS simulations are performed for unsteady laminar flow over a two-dimensional circular cylinder, turbulent flow over a three-dimensional sphere, and massively separated flow over a Martian helicopter rotor airfoil section. Results show a reduction in computational cost, with approximately one-quarter of the number of degrees of freedom relative to a non-adaptive case. The Frobenius norm method performs consistently well for all applications, and is identified as being a preferred method when compared to the vorticity and maximum eigenvalue approaches.
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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