Immersed boundaries in the discontinuous Galerkin spectral element method through hp-adaptivity
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Bibliographic record
Abstract
The immersed boundary method is a promising numerical technique that allows for modeling of complex geometries without the need for body conforming meshes. However, immersed boundary methods present a significant reduction in accuracy. In this paper, we implement the volume penalty method in an hp-adaptive discontinuous Galerkin spectral method framework to solve the two-dimensional acoustic wave equation with immersed boundaries. We demonstrate that combining low porosity, which represents the immersed boundary, with hp-adaptivity reduces oscillations, localizes error to the vicinity of the immersed boundary and improves the overall accuracy. A variety of test cases are presented to show that the implementation is capable of modeling wave propagation in complex geometries with simple Cartesian grids.
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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