Adaptive Discontinuous-Galerkin Reduced-Basis Reduced-Quadrature Method for Many-Query CFD Problems
Bibliographic record
Abstract
View Video Presentation: https://doi.org/10.2514/6.2021-2716.vid We present a projection-based model reduction method for efficient solution of computational fluid dynamics problems in many-query scenarios, which require the evaluation of quantities of interest for many different flow-condition, geometry, or model parameters. Our goal is to construct reduced models that provide rapid and accurate output predictions and the associated a posteriori error estimates. To achieve this goal, our framework builds on the following key ingredients of adaptive high-order methods: the discontinous Galerkin method, which provides stability for conservation laws; the dual-weighted residual method, which provides effective output a posteriori error estimates. In addition, we incorporate two model reduction ingredients: reduced bases, which provide low-dimensional empirical approximation spaces tailored for the specific parametrized problem; reduced quadrature rules, which are the tailored quadrature rules for the reduced bases constructed using an empirical quadrature procedure. Both reduced bases and reduced quadrature rules are identified through an efficient and automatic offline training procedure that is informed by the behavior of a posteriori error estimates. We demonstrate the efficacy and versatility of the model reduction approach in four aerodynamics problems: Reynolds-averaged Navier-Stokes (RANS) flow over the ONERA M6 wing with the Mach number and the angle of attack as the parameters; laminar flow over shape-parametrized airfoils; uncertainty quantification of RANS flow with variabilities in the empirical parameters of the Spalart-Allmaras turbulence model; and unsteady flow past NACA0012 with the Reynolds number as the parameter. The reduced models achieve ~300-20000 speedup at less than 1% drag error level relative to an adaptive DG method and provide effective error estimates.
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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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".