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

TL;DR

This paper introduces FD-NILSS, a non-intrusive algorithm for sensitivity analysis in chaotic systems that is easy to implement and computationally efficient, demonstrated on a 3-D cylinder flow.

Contribution

The paper develops FD-NILSS, a novel non-intrusive method for sensitivity analysis that does not require tangent solvers and can be integrated with existing simulation software.

Findings

FD-NILSS accurately computes sensitivities in chaotic flow.

The computational cost is comparable to the original simulation.

The method is applicable to complex 3-D turbulent flows.

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.