Parametric Reduced-Order Models

We address the problem of propagating input uncertainties through a computational fluid dynamics model. Methods such as Monte Carlo simulation can require many thousands (or more) of computational fluid dynamics solves, rendering them prohibitively expensive for practical applications. This expense can be overcome with reduced-order models that preserve the essential flow dynamics. The specific contributions of this paper are as follows: first, to derive a linearized computational fluid dynamics model that permits the effects of geometry variations to be represented with an explicit affine function; second, to propose an adaptive sampling method to derive a reduced basis that is effective over the joint probability density of the geometry input parameters. The method is applied to derive efficient reduced models for probabilistic analysis of a two-dimensional problem governed by the linearized Euler equations. Reduced-order models that achieve 3-orders-of-magnitude reduction in the number of states are shown to accurately reproduce computational fluid dynamics Monte Carlo simulation results at a fraction of the computational cost.