Integrating a Stabilized Radial Basis Function Method with Lattice Boltzmann Method
Bibliographic record
Abstract
The lattice Boltzmann method (LBM) has two key steps: collision and streaming. In a conventional LBM, the streaming is exact, where each distribution function is perfectly shifted to the neighbor node on the uniform mesh arrangement. This advantage may curtail the applicability of the method to problems with complex geometries. To overcome this issue, a high-order meshless interpolation-based approach is proposed to handle the streaming step. Owing to its high accuracy, the radial basis function (RBF) is one of the popular methods used for interpolation. In general, RBF-based approaches suffer from some stability issues, where their stability strongly depends on the shape parameter of the RBF. In the current work, a stabilized RBF approach is used to handle the streaming. The stabilized RBF approach has a weak dependency on the shape parameter, which improves the stability of the method and reduces the dependency of the shape parameter. Both the stabilized RBF method and the streaming of the LBM are used for solving three benchmark problems. The results of the stabilized method and the perfect streaming LBM are compared with analytical solutions or published results. Excellent agreements are observed, with a little advantage for the stabilized approach. Additionally, the computational cost is compared, where a marginal difference is observed in the favor of the streaming of the LBM. In conclusion, one could report that the stabilized method is a viable alternative to the streaming of the LBM in handling both simple and complex geometries.
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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) | 0.000 | 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".