CFD stability improvement using dynamic mode decomposition of solution update vectors
Bibliographic record
Abstract
We present a novel method for improving the numerical stability of finite volume simulations by optimizing the mesh through dynamic mode decomposition of solution update vectors. Our approach leverages dynamic mode decomposition to approximate the non-linear solution evolution as a linear mapping, enabling us to represent the dynamic system with fewer degrees of freedom. By conducting eigenanalysis on the reduced system, we gain insights into the growth rate and oscillation frequency of dominant solution modes. We then identify the control volumes and vertices that have a significant influence on each dynamic solution mode. We compute the gradients of the Jacobian diagonal elements with respect to the movement of the selected vertices. Based on these gradients, we adjust the positions of the vertices to improve the diagonal dominance of the corresponding Jacobian rows. We utilize this approach in conjunction with our in-house flow solver as well as with Ansys Fluent to test its effectiveness when applied to different types of CFD software architecture. We show that the presented methodology is fully non-invasive to the host flow solver and does not require any modifications or access to the source code. Our approach offers a substantial computational cost reduction compared to existing methods for numerical stability improvement. Various results demonstrate the strength and efficacy of this state-of-the-art approach for improving numerical stability through mesh optimization.
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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) | 0.001 | 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) | 0.004 | 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".