Sensitivity analysis on chaotic dynamical systems by Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS)

Abstract

We present the Finite Difference Non-Intrusive Least Squares Shadowing (FD-NILSS) algorithm for computing sensitivities of long-time averaged quantities in chaotic dynamical systems. FD-NILSS does not require tangent solvers, and can be implemented with little modification to existing numerical simulation software. We also give a formula for solving the least-squares problem in FD-NILSS, which can be applied in NILSS as well. Finally, we apply FD-NILSS for sensitivity analysis of a chaotic flow over a 3-D cylinder at Reynolds number 525, where FD-NILSS computes accurate sensitivities and the computational cost is in the same order as the numerical simulation.

20 pages, 8 figures

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• Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS)
• Adjoint shadowing directions in hyperbolic systems for sensitivity analysis
• Approximating linear response by nonintrusive shadowing algorithms
• Windowing Regularization Techniques for Unsteady Aerodynamic Shape Optimization
• Fast differentiation of hyperbolic chaos
• Adjoint-based trailing edge shape optimization of a transonic turbine vane using large eddy simulations