Stability of Energy Stable Flux Reconstruction on Generalized Three-dimensional Curvilinear Grids for Linear Advection
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Bibliographic record
Abstract
The flux reconstruction method initially proposed by H.T. Huynh in his seminal paper, 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. The attraction of the method follows with its stability proofs for the linear advection problem on linear elements, under a class of energy stable flux reconstruction (ESFR) schemes also known as Vincent-Castonguay-Jameson-Huynh (VCJH) schemes. This paper expands the proof to three-dimensional curvilinear elements with nonlinear Jacobians. Additionally, by considering ESFR as a filtered DG scheme, this paper shows a trivial way to solve for the correction functions along faces with nonlinear Jacobians. Also, this paper verifies that the ESFR schemes can in fact be taken as a filtered DG scheme in both strong and weak forms. The main result of this paper is that the energy stability criteria for three-dimensional curvilinear elements results identically to the linear one-dimensional ESFR strong form case for both the ESFR strong and weak forms.
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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