The control of the displacement of a passive particle in a point vortex flow

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Balsa, C (Author) Other; Sílvio Gama (Author) FCUP

Journal

Title: Journal of Computational Methods in Sciences and Engineering

Vol. 21

Pages: 1215-1229

ISSN: 1472-7978

Publisher: IOS PRESS

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 1215 Citations

Other information

Authenticus ID: P-00T-PV7

DOI: 10.3233/jcm-204710

Abstract (EN): This work reports numerical explorations in advection of one passive tracer by point vortices living in the unbounded plane. The main objective is to find the energy-optimal displacement of one passive particle (point vortex with zero circulation) surrounded by N point vortices. The direct formulation of the corresponding control problems is presented. The restrictions are due to (i) the ordinary differential equations that govern the displacement of the passive particle around the point vortices, (ii) the available time T to go from the initial position z(0) to the final destination z(f), and (iii) the maximum absolute value u(max) that is imposed on the control variables. The latter consist in staircase controls, i.e., the control is written as a finite linear combination of characteristic functions on the real interval. The resulting optimization problems are solved numerically. The numerical results shows the existence nearly/quasi optimal control for the cases of N = 1, N = 2, N = 3, and N = 4 vortices.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15