Nonlinearly Stable Split Forms for the Weight-Adjusted Flux Reconstruction High-Order Method: Curvilinear Numerical Validation
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Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2022-0190.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 Burgers' equation through the incorporation of the ESFR correction functions on the volume terms. Unfortunately, this requires inverting a dense matrix in every element for curvilinear coordinates. This paper presents a low-storage, weight-adjusted approach for discretely entropy stable FR schemes in curvilinear coordinates. The theoretical results are verified with convective flow in curvilinear coordinates.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 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 |
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Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
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