Conservative Immersed Boundary Methods on Cartesian grids for inviscid compressible flows simulation
Bibliographic record
Abstract
This work introduces three conservative methods based on the Immersed Boundary Method. These methods make use of cut-cells to ensure the conservation properties in the numerical solution. However, since some cut-cells can be very small, they can significantly restrict the time step of an explicit time integration scheme. To circumvent this limitation, a semi-implicit treatment of the small cells is employed. The first method relies on a straightforward flux redistribution procedure that globally restores conservation on the cut-cells grid. The other two methods employ the local conservative discretization form of the finite volume method, along with optimization procedures, to ensure local conservation of the numerical solution within each cell. These methods have been tested on two-dimensional inviscid compressible flow problems, demonstrating results comparable to those obtained with the standard Cut-Cells method in terms of accuracy and conservation. Furthermore, the methods are stable and can be effectively used with an explicit time integration scheme without encountering any stability issues related to the small cut-cells. • Conservative methods based on the Immersed Boundary Method using a cut-cells grid. • Achieved stable treatment of small cells through a reconstruction procedure. • Application of the new methods to 2D inviscid compressible flow problems. • Demonstrated conservation and accuracy comparable to the Cut-Cells method. • Superior capture of shocks compared to the traditional Immersed Boundary Method.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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 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".