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

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.