A conservative finite volume cut-cell method on an adaptive Cartesian tree grid for moving rigid bodies in incompressible flows
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Bibliographic record
Abstract
We present here a conservative finite volume cut-cell method for moving rigid bodies immersed in incompressible flows, implemented in the open-source software Basilisk. The method is constructed starting from a uniform Cartesian grid, in which we embed a discrete representation of a rigid body that intersects underlying cells to form irregular fluid control volumes, or cut-cells. In each cell, we then discretize the Navier-Stokes equations using a fractional-step projection method and insure that at each time step, the finite volume discretization scheme remains spatially second-order and conservative in cut-cells by carefully computing gradients normal to the embedded boundaries, even in degenerated cases. To avoid stability issues due to the well-documented problem of small cut-cells, we use a simple and efficient flux redistribution technique to extend the range of influence of small cut-cells to their neighboring cells. We also provide a time history to emerged cells through a field value reconstruction in the direction normal to the embedded boundaries. In case of freely moving particles, we simply use an explicit weak fluid-solid coupling strategy. Finally, we robustly extend our conservative finite volume cut-cell method for moving boundaries to adaptive Cartesian tree grids by constructing specific restriction and prolongation operators between two consecutive levels of a tree grid in the vicinity of a cut-cell. We successfully test the method on a series of validation test cases ranging from fixed, moving with a prescribed motion to freely moving 2D cylinders and spheres for a wide range of Reynolds (0 ≤ Re ≤ 1000) and Galileo numbers (0 ≤ Ga ≤ 250). While the method is accurate, conservative, robust and efficient, we show that a low-amplitude pressure noise is generated when using mesh adaptation in the limit case of very high Reynolds numbers.
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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 | 0.005 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.003 | 0.002 |
| 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.
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