Imperial College London
Alternate

Dr. Yongyun Hwang

Faculty of Engineering, Department of Aeronautics

Reader in Fluid Mechanics
 
 
 
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Contact

 

+44 (0)20 7594 5078y.hwang

 
 
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Location

 

337City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Lakshmi:2020:10.1137/19M1267647,
author = {Lakshmi, MV and Fantuzzi, G and Fernández-Caballero, JD and Yongyun, H and Chernyshenko, S and Lakshmi, M and Fantuzzi, G and Fernández-Caballero, J and Hwang, Y and Chernyshenko, S},
doi = {10.1137/19M1267647},
journal = {SIAM Journal on Applied Dynamical Systems},
pages = {763--787},
title = {Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear ow},
url = {http://dx.doi.org/10.1137/19M1267647},
volume = {19},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Tobasco et al. [Phys. Lett. A, 382:382–386, 2018] recently suggested that trajectories of ODE systems that optimize the innite-time average of a certain observable can be localized using sublevel sets of a function that arise when bounding such averages using so-called auxiliary functions. In this paper we demonstrate that this idea is viable and allows for the computation of extremal unstable periodic orbits (UPOs) for polynomial ODE systems. First, we prove that polynomial optimization is guaranteed to produce auxiliary functions that yield near-sharp bounds on time averages, which is required in order to localize the extremal orbit accurately. Second, we show that points inside the relevant sublevel sets can be computed eciently through direct nonlinear optimization. Such points provide good initial conditions for UPO computations. As a proof of concept, we then combine these methods with a single-shooting Netwon–Raphson algorithm to study extremal UPOs for a nine-dimensional model of sinusoidally forced shear ow. We discover three previously unknown families of UPOs, one of which simultaneously minimizes the mean energy dissipation rate and maximizes the mean perturbation energy relative to the laminar state for Reynolds numbers approximately between 81.24 and 125.
AU  - Lakshmi,MV
AU  - Fantuzzi,G
AU  - Fernández-Caballero,JD
AU  - Yongyun,H
AU  - Chernyshenko,S
AU  - Lakshmi,M
AU  - Fantuzzi,G
AU  - Fernández-Caballero,J
AU  - Hwang,Y
AU  - Chernyshenko,S
DO  - 10.1137/19M1267647
EP  - 787
PY  - 2020///
SN  - 1536-0040
SP  - 763
TI  - Finding extremal periodic orbits with polynomial optimization, with application to a nine-mode model of shear ow
T2  - SIAM Journal on Applied Dynamical Systems
UR  - http://dx.doi.org/10.1137/19M1267647
UR  - https://arxiv.org/abs/1906.04001v1/
UR  - https://epubs.siam.org/doi/10.1137/19M1267647
UR  - http://hdl.handle.net/10044/1/78019
VL  - 19
ER  -
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