Parametric Reduced-Order Models for Probabilistic Analysis of Unsteady Aerodynamic Applications

Methodology is presented to derive reduced-order models for large-scale parametric applications in unsteady aerodynamics. The specific case considered in this paper is a computational fluid dynamic (CFD) model with parametric dependence that arises from geometric shape variations. The first key contribution of the methodology is the derivation of a linearized model that permits the effects of geometry variations to be represented with an explicit affine function. The second key contribution is an adaptive sampling method that utilizes an optimization formulation to derive a reduced basis that spans the space of geometric input parameters. The method is applied to derive efficient reduced-order models for probabilistic analysis of the effects of blade geometry variation for a two-dimensional model problem governed by the Euler equations. Reduced-order models that achieve three orders of magnitude reduction in the number of states are shown to accurately reproduce CFD Monte Carlo simulation results at a fraction of the computational cost. I.