Sensitivity computation of statistically stationary quantities in turbulent flows
© 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....
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| Format: | Article |
| Language: | English |
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American Institute of Aeronautics and Astronautics
2021
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| Online Access: | https://hdl.handle.net/1721.1/138090 |
| _version_ | 1826197040413016064 |
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| author | Chandramoorthy, Nisha Wang, Qiqi |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Chandramoorthy, Nisha Wang, Qiqi |
| author_sort | Chandramoorthy, Nisha |
| collection | MIT |
| description | © 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. |
| first_indexed | 2024-09-23T10:41:46Z |
| format | Article |
| id | mit-1721.1/138090 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T10:41:46Z |
| publishDate | 2021 |
| publisher | American Institute of Aeronautics and Astronautics |
| record_format | dspace |
| spelling | mit-1721.1/1380902023-02-08T18:50:23Z Sensitivity computation of statistically stationary quantities in turbulent flows Chandramoorthy, Nisha Wang, Qiqi Massachusetts Institute of Technology. Department of Mechanical Engineering Massachusetts Institute of Technology. Department of Aeronautics and Astronautics © 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. 2021-11-09T21:57:07Z 2021-11-09T21:57:07Z 2019-06 2021-05-04T18:03:17Z Article http://purl.org/eprint/type/ConferencePaper https://hdl.handle.net/1721.1/138090 Chandramoorthy, Nisha and Wang, Qiqi. 2019. "Sensitivity computation of statistically stationary quantities in turbulent flows." AIAA Aviation 2019 Forum. en 10.2514/6.2019-3426 AIAA Aviation 2019 Forum Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf American Institute of Aeronautics and Astronautics arXiv |
| spellingShingle | Chandramoorthy, Nisha Wang, Qiqi Sensitivity computation of statistically stationary quantities in turbulent flows |
| title | Sensitivity computation of statistically stationary quantities in turbulent flows |
| title_full | Sensitivity computation of statistically stationary quantities in turbulent flows |
| title_fullStr | Sensitivity computation of statistically stationary quantities in turbulent flows |
| title_full_unstemmed | Sensitivity computation of statistically stationary quantities in turbulent flows |
| title_short | Sensitivity computation of statistically stationary quantities in turbulent flows |
| title_sort | sensitivity computation of statistically stationary quantities in turbulent flows |
| url | https://hdl.handle.net/1721.1/138090 |
| work_keys_str_mv | AT chandramoorthynisha sensitivitycomputationofstatisticallystationaryquantitiesinturbulentflows AT wangqiqi sensitivitycomputationofstatisticallystationaryquantitiesinturbulentflows |