Computing Viscous Flow Along a 2D Open Channel Using the Immersed Interface Method
Bibliographic record
Abstract
We present a numerical method for simulating 2D flow through a channel with deformable walls. The fluid is assumed to be incompressible and viscous. We consider the highly viscous regime, where fluid dynamics are described by the Stokes equations, and the less viscous regime described by the Navier-Stokes equations. The model is formulated as an immersed boundary problem, with the channel defined by compliant walls that are immersed in a larger computational fluid domain. The channel traverses through the computational domain, and the walls do not form a closed region. When the walls deviate from their equilibrium position, they exert singular forces on the underlying fluid. We compute the numerical solution to the model equations using the immersed interface method, which preserves sharp jumps in the solution and its derivatives. The immersed interface method typically requires a closed immersed interface, a condition that is not met by the present configuration. Thus, a contribution of the present work is the extension of the immersed interface method to immersed boundary problems with open interfaces. Numerical results indicate that this new method converges with second-order accuracy in both space and time, and can sharply capture discontinuities in the fluid solution.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".