Optimal Control of a Passive Particle Advected by a Lamb-Oseen (Viscous) Vortex

• Type: Article in International Scientific Journal
• Date: 2022

Authors

Marques, G (Author) Other; Sílvio Gama (Author) FCUP; Pereira, FL (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: COMPUTATION

Vol. 12

Final page: 87

ISSN: 2079-3197

Publisher: MDPI

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 2 Citations

Other information

Authenticus ID: P-00W-KTM

DOI: 10.3390/computation10060087

Abstract (EN): This work concerns the optimal control of a passive particle in viscous flows. This is relevant since, while there are many studies on optimal control in inviscid flows, there is little to no work in this context for viscous flows, and viscosity cannot always be neglected. Furthermore, in many tasks, there is a need to reduce the energy spent; thus, energy-optimal solutions to problems are important. The aim of this work is to investigate how to optimally move a passive particle advected by a Lamb-Oseen (viscous) vortex between two given points in space in a given time interval while minimising the energy spent on this process. We take a control acting only on the radial component of the motion, and, by using the Pontryagin's Maximum Principle, we find an explicit time-dependent extremal. We also analyse how the energy cost changes with the viscosity of the flow.The problem is transformed into a parameter search problem with two parameters related to the radial and angular coordinates of the initial point. The energy cost of the process increases with viscosity as long as the passive particle maintains the number of full turns it makes around the vortex. However, the energy cost increases if the increase in viscosity forces the particle to make fewer full revolutions around the vortex.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 13