DTE AICCOMAS 2025

Building-Block Model Aggregation: Reduction of Turbulence Modeling Uncertainties via Bayesian Inference and Machine Learning

  • Roques, Cécile (Sorbonne Université)
  • Dergham, Grégory (Safran Tech)
  • Merle, Xavier (Arts et Métiers Institute of Technology)
  • Cinnella, Paola (Sorbonne Université)

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Despite decades of work, there is no consensus on closure models for solving the Reynolds Averaged Navier-Stokes (RANS) equations, which are the cornerstone for high Reynolds number flow simulations. Building on XMA, we introduce BBMA: Building Block Model Aggregation, a methodology that mixes solutions from a set of competing RANS models calibrated to capture fundamental turbulent flow processes, to quantify and reduce structural and parametric uncertainties associated with turbulence modelling choices. In detail, the underlying idea is that a complex flow exhibits subregions dominated by simpler dynamical processes. We then define “building block” data sets corresponding to typical fundamental processes (attached boundary layer, separation region, wake...) and we use Bayesian calibration to generate a set of “expert” RANS models specialized at capturing each flow topologies. A Random Forests Regressor is then trained from additional data to build a model mixture, i.e. to learn a relationship that assigns weights to the component models, depending on the detected local dynamics within a more complex flow. The models are assigned higher or lower weights according to their likelihood of capturing the local dynamics, and the inter-model variance is used to quantify the modelling uncertainty. To make the mixture generalizable to unseen flows, the regression relies on a set of local input flow features instead of the geometrical coordinates. The proposed methodology is applied to the prediction of a 3D turbomachinery configuration, and specifically the flow around a linear compressor cascade of NACA V65 blades. Four baseline models, namely, the Spalart-Allmaras and the k-l models along with linear (LCR) or quadratic (QCR) constitutive relations for the Reynolds stress tensor are used to build the mixture. The models are first calibrated independently using experimental observations for four building-block flow scenarios (zero-pressure gradient flat plate flow, square duct flow, separated flow behind a backward-facing step, and far wake flow), using surrogate-model-assisted Bayesian inference with advanced MCMC Carlo sampling. Afterwards, the resulting expert models are aggregated by learning their weights from higher fidelity simulations of the NACA V65 cascade [3]. The BBMA is shown to outperform the baseline and the expert models in predicting the flow from which training data were extracted, and it shows promise in generalizing to unseen flow conditions.