Entropy Stable Weight-Adjusted Flux Reconstruction High-Order Method in Split Form for Compressible Flows on Curvilinear Grids
Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2023-0666.vid The flux reconstruction method has gained popularity in the research community as it recovers promising high-order methods through modally filtered correction fields, such as the Discontinuous Galerkin (DG) method, on unstructured grids over complex geometries. Under a class of energy stable flux reconstruction (ESFR) schemes, the flux reconstruction method allows for larger time-steps than DG while ensuring stability for linear advection on linear elements. For nonlinear problems, split forms emerged as the popular approach proving stability for unsteady problems on coarse unstructured grids; with recent developments proving stability for the one-dimensional Burgers' equation through the incorporation of the ESFR correction functions on the volume terms. In curvilinear coordinates, the metric terms also add a nonlinearity to the scheme in reference space. This paper is the first to combine both the nonlinearity from the governing equation along with the nonlinearity from the curvilinear metric terms for nonlinearly stable flux reconstruction. Unfortunately, in curvilinear coordinates, the scheme requires that the dense mass matrix is inverted in every element. This paper incorporates a low-storage, weight-adjusted approach to approximate the inverse of the mass matrix, while preserving the desired nonlinear stability property. The theoretical results are verified with the inviscid Taylor-Green vortex problem on a coarse, non-symmetrically warped curvilinear grid.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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".