Sensitivity computation of statistically stationary quantities in turbulent flows
Name
1905.09362.pdf
Description
Accepted version
Size
480.97 KB
Format
Adobe PDF
Checksum (MD5)
d009b7c39fd4ae95969e40121117b119
Author(s)
Chandramoorthy, Nisha
Wang, Qiqi
Date Issued
June 2019
Journal
AIAA Aviation 2019 Forum
Publisher
American Institute of Aeronautics and Astronautics
Citation
Chandramoorthy, Nisha and Wang, Qiqi. 2019. "Sensitivity computation of statistically stationary quantities in turbulent flows." AIAA Aviation 2019 Forum.
Version
Author's final manuscript
Abstract
© 2019, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. It is well-known that linearized perturbation methods for sensitivity analysis, such as tangent or adjoint equation-based, finite difference and automatic differentiation are not suitable for turbulent flows. The reason is that turbulent flows exhibit chaotic dynamics, leading to the norm of an infinitesimal perturbation to the state growing exponentially in time. As a result, these conventional methods cannot be used to compute the derivatives of long-time averaged quantities to control or design inputs. The ensemble-based approaches [1, 2] and shadowing-based approaches ([3–5]) to circumvent the problems of the conventional methods in chaotic systems, also suffer from computational impracticality and lack of consistency guarantees, respectively. We introduce the space-split sensitivity, or the S3 algorithm, that is a Monte-Carlo approach to the chaotic sensitivity computation problem. In this work, we derive the S3 algorithm under simplifying assumptions on the dynamics and present a numerical validation on a low-dimensional example of chaos.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.2514/6.2019-3426
