Least-Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Abstract

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics: most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, called least-squares shadowing, avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of least-squares shadowing to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The least-squares shadowing sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current least-squares shadowing implementation is high.