Data-Driven POD-Galerkin Reduced Order Model for Turbulent Flows

TL;DR

This work tackles the computational bottleneck of simulating turbulent flows by introducing a hybrid ROM (Mixed-ROM) that preserves projection-based velocity and pressure reduction while non-intrusively modeling the eddy viscosity with Radial Basis Function interpolation. The approach delivers accurate steady and unsteady flow predictions up to Re ~ 1e5, with notable improvements in pressure fields and lift coefficients compared to purely projection-based ROMs, and achieves substantial speedups. By decoupling turbulence closure from the reduced velocity/pressure spaces, the method maintains robustness across different turbulence models (e.g., k-ε and SST k-ω) and solver implementations. The results indicate strong potential for real-time prototyping, optimization, and control in CFD applications, with clear avenues for further enhancement using neural networks and alternative data-driven closures.

Abstract

In this work we present a Reduced Order Model which is specifically designed to deal with turbulent flows in a finite volume setting. The method used to build the reduced order model is based on the idea of merging/combining projection-based techniques with data-driven reduction strategies. In particular, the work presents a mixed strategy that exploits a data-driven reduction method to approximate the eddy viscosity solution manifold and a classical POD-Galerkin projection approach for the velocity and the pressure fields, respectively. The newly proposed reduced order model has been validated on benchmark test cases in both steady and unsteady settings with Reynolds up to Re=O(10^5).

Figures (24)

• Figure 1: Sketch of a finite volume in 2 dimensions
• Figure 2: The computational domain used in the numerical simulations, all lengths are described in terms of the characteristic length $D$ that is equal to $1$ meter.
• Figure 3: Cumulative ignored eigenvalues decay. In the plot, the solid red line refers to the velocity eigenvalues, the dashed black line indicates the pressure eigenvalues and the dash-dotted blue line finally refers to the eddy viscosity eigenvalues.
• Figure 4: $k-\epsilon$ turbulence model case, velocity fields for the value of the parameter $U = 7.0886$ m s: (a) shows the FOM velocity, while in (b) one can see the P-ROM velocity, and finally in (c) we have the Mixed-ROM velocity.
• Figure 5: $k-\epsilon$ turbulence model case, pressure fields for the value of the parameter $U = 7.0886$ m s: (a) shows the FOM pressure, while in (b) one can see the P-ROM pressure, and finally in (c) we have the Mixed-ROM pressure.