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Control problem in passive tracer advection by point vortex flow: a case study
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Orientador(es)
Resumo(s)
Vortex dynamics and passive tracers in vortex-dominated flows form a vast area of
research that continues to attract the attention of numerous studies. Among these studies, it
has emerged in recent times a special interest in the use of control theory applied to vortex
dynamics. Point vortices are singular solutions of the two-dimensional incompressible Euler
equations. These solutions correspond to the limiting case where the vorticity is completely
concentrated on a finite number of spatial points, each with a prescribed strength/circulation.
By definition, a passive tracer is a point vortex with zero circulation. We are concerned with the
dynamics of a passive tracer advected by two-dimensional point vortex flow. More precisely,
we want to drive a passive particle from an initial starting point to a final terminal point, both
given a priori, in a given finite time. The flow is originated by the displacement of N viscous
point vortices. More precisely, we look for the optimal trajectories that minimize the objective
function that corresponds to the energy expended in the control of the trajectories. The restrictions are essentially due to the ordinary differential equations that govern the displacement of
the passive particle around the viscous point vortices.
Descrição
Palavras-chave
Point vortex flow Passive tracer Control problem Numerical optimization
Contexto Educativo
Citação
Balsa, Carlos; Gama, Sílvio; Braz-César, M.T. (2019). Control problem in passive tracer advection by point vortex flow: a case study. In 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering. Crete, Greece. p. 3495-3509
Editora
ECCOMAS