Immersed boundary conditions method for heat conduction problems in slots with time‐dependent geometry
Bibliographic record
Abstract
SUMMARY A grid‐less, fully implicit, spectrally accurate algorithm for solving three‐dimensional, both stationary and time‐dependent, heat conduction problems in slots formed by either fixed or time‐dependent boundaries has been developed. The algorithm is based on the concept of immersed boundary conditions (IBC), where the physical domain is immersed within the computational domain and the boundary conditions take the form of internal constraints. The IBC method avoids the need to construct adaptive, time‐dependent grids resulting in the reduction of the required computational resources and, at the same time, maintaining accurate information about the location of the boundaries. The algorithm is spectrally accurate in space and capable of delivering first‐, second‐, third‐ and fourth‐order accuracy in time. Given a potentially large size of the resultant linear algebraic system, various methods that take advantage of the special structure of the coefficient matrix have been explored in search for an efficient solver, including a specialized direct solver as well as serial and parallel iterative solvers. The specialized direct solver has been found to be the most efficient from the viewpoints of the speed of the computations and the memory requirements. Copyright © 2010 John Wiley & Sons, Ltd.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".