Mesh Optimization for Improved Computational Fluid Dynamics Numerical Stability and Convergence Rate
Bibliographic record
Abstract
A novel mesh optimization approach is utilized in conjunction with the Ansys Fluent solver for numerical stability and convergence rate enhancement of computational fluid dynamics simulations. This method leverages the dynamic mode decomposition of solution update vectors for solution mode identification. Through this data reduction technique, the large-scale linear evolution system is mapped onto a smaller space with substantially fewer degrees of freedom for stability analysis at a negligible fraction of the overall computational cost. The eigenanalysis of the small-scale matrix facilitates the identification of dominant solution modes during the simulation. This mesh optimization technique leverages the gradients of the problematic solution modes with respect to local changes of the mesh to calculate proper modification vectors for a small collection of nodes. These modifications lead to the improved numerical stability of the simulation. Employing the Ansys Fluent CFD package as the primary finite-volume solver, our study demonstrates the complete non-invasiveness of the presented mesh optimization approach, requiring no access to the underlying software architecture. The results presented herein illustrate the feasibility and efficacy of this mesh optimization technique in improving numerical stability and convergence rate, showcasing its compatibility with third-party flow solvers.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| 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".