Comparison of Second-Order Derivatives and Metamodel-Based Monte-Carlo Approaches to Estimate Statistics for Robust Design of a Transonic Wing

Abstract

We present two different practical methods to estimate the drag uncertainty in Computational Fluid Dynamics (CFD), used to solve robust design optimization problems. We aim at taking into account the varability of operational conditions, such as Mach number and angle of attack and we want to estimate statistical quantities (mean and variance) of the drag coefficient by propagating uncertainties through the CFD code. In order to avoid the prohibitively expensive Monte Carlo analysis for CFD applications, we compare two approximate approaches to estimate statistics: a perturbative approach (Method of Moment) in which the first- and second-order derivatives of the drag coefficient are obtained using Automatic Differentiation (AD), and a metamodel-based approach in which the response surface is built from a database. In order to compare the accuracy, the computational efficiency and the implementation difficulties of the proposed methods, a practical testcase in the context of three-dimensional Eulerian flow is presented: a subsonic, transonic and fish-tail transonic flow around the wing of a business aircraft subject to uncertain operative conditions in terms of Mach number and incidence angle.

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