Efficient and Accurate Surrogate Modeling of Turbulent Flows via Space-Dependent Aggregation and Reduced Order Models

Abstract

Reynolds-Averaged Navier-Stokes (RANS) models are widely used for turbulent flow simulations due to their computational efficiency, but their accuracy strongly depends on the selected turbulence closure and may vary across the flow domain. Space-dependent model aggregation has been shown to improve RANS predictions by combining multiple turbulence models, although at the cost of repeated high-fidelity simulations. The first novelty of this work is a unified framework that combines different turbulence models, space-dependent aggregation, and non-intrusive reduced order models to achieve both accuracy and efficiency. Two aggregation pipelines are proposed: a Mixed FOM-ROM (MFR) approach, where a reduced order model is trained on aggregated RANS solutions, and a Mixed-ROM (MR) approach, which directly aggregates multiple reduced order models built on top of different RANS full-order models. The second novelty is that the aggregation weights are learned via a neural-network that provides smooth, space-continuous weights and improves generalization with respect to standard weighting techniques. The resulting surrogate models are validated on the two-dimensional periodic hill benchmark and on the flow over a height-dependent bump, demonstrating improved accuracy over individual RANS and ROM predictions at near real-time computational cost.

Figures (18)

• Figure 1: Schematic representation of the mixed aggregation pipelines.
• Figure 2: Test case 1. Schematic representation of the geometrical parametrization of the computational domain. Hill profiles corresponding to three different values of the hill stretch factor $\alpha$ are illustrated. The quantity $L_c$ indicates the streamwise extent of the curved regions of the hill profile for the case $\alpha=1$.
• Figure 3: Test case 1. Deformed representations of the periodic hill configurations with $\alpha=0.5$ and $L_x/H=7.071$ (top), $\alpha=1.0$ and $L_x/H=9.0$ (middle) and with $\alpha=1.0$ and $L_x/H=12.0$ (bottom).
• Figure 4: Test case 1. Comparison of velocity profiles obtained from RANS simulations using different turbulence models and DNS reference data. We display the horizontal component of the velocity field, extracted at ten distinct downstream locations. The results correspond to the test configuration with $\alpha=1.25$ and $L_x/H=9.96$. The light blue area indicates the envelope of all the different RANS simulations.
• Figure 5: Test case 1. Comparison of relative test errors with respect to DNS data for baseline RANS models and surrogate model mixtures.

Theorems & Definitions (4)

• Remark 3.1
• Remark 4.1
• Remark 4.2
• Remark 4.3