On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics

This article addresses the delicate issue of estimating physical uncertainties in aerodynamics. Usually, flow simulations are performed in a fully deterministic approach, although in real life operational uncertainty arises due to unpredictable factors that alter the flow conditions. In this article, we present and compare two methods to account for uncertainty in aerodynamic simulation. Firstly, automatic differentiation tools are used to estimate first- and second-order derivatives of aerodynamic coefficients with respect to uncertain variables, yielding an estimate of expectation and variance values (Method of Moments). Secondly, metamodelling techniques (radial basis functions, kriging) are employed in conjunction with Monte-Carlo simulations to derive statistical information. These methods are demonstrated for 3D Eulerian flows around the wing of a business aircraft at different regimes subject to uncertain Mach number and angle of attack.