Reduced-Basis Multifidelity Approach for Efficient Parametric Study of NACA Airfoils

Multifidelity methods are often used to reduce the cost of parameter space exploration, with applications to design optimization and uncertainty quantification. We present a multifidelity method to construct a reduced-basis representation of spatially (or temporally) varying solution fields and use it to explore the effect of variation in the geometry and angle of attack on the pressure coefficient response of a two-dimensional NACA 4412 airfoil in steady, incompressible flow at Re = 1.52 Million. Two low-fidelity simulations use 1) Euler flow and 2) coarse-mesh Spalart-Allmaras Reynolds-averaged Navier-Stokes (RANS) with unresolved boundary layers. Each low-fidelity model is paired with a high-fidelity RANS model, to construct two multifidelity models that approximate the high-fidelity response associated with a set of parametric realizations. The predictive capacity and efficiency of both multifidelity models are analyzed and found to perform well for this combination of aerodynamic system and parameter space. In particular, the bifidelity model based on Euler flow predicts high-fidelity RANS results within 1.6% error at a cost that is 50 times less. Such a cost reduction demonstrates the utility of this method for industrial-scale design optimization and uncertainty quantification problems.