Non-Intrusive Polynomial Chaos Method Applied to Full-Order and Reduced Problems in Computational Fluid Dynamics: a Comparison and Perspectives

TL;DR

The paper investigates uncertainty quantification in CFD by applying non-intrusive Polynomial Chaos Expansion (PCE) to a flow around a NACA airfoil with uncertain angle of attack $\alpha$ and inflow speed $U$, comparing a full-order OpenFOAM solver with a POD-Galerkin reduced order model (ROM). PCE coefficients are obtained via regression, and the authors assess how ROM-based outputs affect PCE accuracy. Results show that, with careful training (including stall-region emphasis), the POD-ROM can capture essential dynamics and, when coupled with PCE, yields comparable predictive performance to FOM-based PCE while reducing computational cost. The study demonstrates a viable, non-intrusive UQ pipeline for CFD and outlines avenues to extend the method to turbulent regimes and more complex boundary treatments.

Abstract

In this work, Uncertainty Quantification (UQ) based on non-intrusive Polynomial Chaos Expansion (PCE) is applied to the CFD problem of the flow past an airfoil with parameterized angle of attack and inflow velocity. To limit the computational cost associated with each of the simulations required by the non-intrusive UQ algorithm used, we resort to a Reduced Order Model (ROM) based on Proper Orthogonal Decomposition (POD)-Galerkin approach. A first set of results is presented to characterize the accuracy of the POD-Galerkin ROM developed approach with respect to the Full Order Model (FOM) solver (OpenFOAM). A further analysis is then presented to assess how the UQ results are affected by substituting the FOM predictions with the surrogate ROM ones.

Figures (17)

• Figure 1: The angle of attack on an airfoil.
• Figure 2: The lift coefficient curve for the airfoil NACA0012.
• Figure 3: (a) The OpenFOAM mesh used in the simulations. (b) A picture of the mesh zoomed near the airfoil.
• Figure 4: The FOM lift coefficient for the first case, as it can be seen in the plot the vast majority of the samples is clustered around $\alpha = 0$.
• Figure 5: The first sampling case : the full order lift coefficients curve versus the ROM reconstructed one with $10$ modes used for each of velocity, pressure and supremizer fields.