Splitting schemes for the stress formulation of fluid–structure interaction problems
Bibliographic record
Abstract
In this article we demonstrate that the novel stress formulation of the Navier–Stokes equations proposed in Minev and Vabishchevich (2018) can be extended to the case of fluid–structure interaction problems. This formulation allows for an easy treatment of the fluid–structure interface boundary conditions. Furthermore, we propose a first order (in time) splitting scheme for this formulation and study its stability in the linear case. It utilizes a level set approach for the interface tracking and regularization of the interface problem. We also demonstrate how this scheme can be extended to the nonlinear case of a neo-Hookean elastic material. The computational complexity of the resulting problem seem to be comparable or better than most available schemes that treat the problem in primitive variables. A downside of such an approach is that it requires a higher than the traditional formulations in terms of primitive unknowns degree of smoothness of the solution for the stress. However, in addition to the solution for the velocity and the stress, it also yields information about the stress tensor, computed with an optimal accuracy. The scheme is demonstrated on two benchmark problems borrowed by other authors, and the results, although computed with a purely linear model look very similarly to the results of other authors that are based on a nonlinear neo-Hookean model.
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".