Two dimensional incompressible ideal flow around a thin obstacle tending to a curve
Incompressible flow around thin obstacle, uniqueness for the wortex-wave system
We present here the results concerning the influence of a thin obstacle on the behavior of incompressible flow. We extend the works made by Itimie, Lopes Filho, Nussenzveig Lopes and Kelliher where they consider that the obstacle shrinks to a point. We begin by working in two-dimension, and thanks to complex analysis we treat the case of ideal and viscous flows around a curve. Next, we consider three-dimensional viscous flow in the exterior of a surface/curve. We finish by giving uniqueness of the...
Fluide idéal incompressible en dimension deux autour d’un obstacle fin
Nous étudions le comportement asymptotique des fluides incompressibles dans les domaines extérieurs, quand l’obstacle devient de plus en plus fin, tendant vers une courbe. Nous étendons les travaux d’Iftimie, Lopes Filho, Nussenzveig Lopes et Kelliher dans lesquels les auteurs considèrent des obstacles se contractant vers un point. En utilisant des outils de l’analyse complexe, nous détaillerons le cas des fluides idéaux en dimension deux autour d’une courbe. Nous donnerons ensuite, à titre indicatif,...
The vortex method for 2D ideal flows in the exterior of a disk
The vortex method is a common numerical and theoretical approach used to implement the motion of an ideal flow, in which the vorticity is approximated by a sum of point vortices, so that the Euler equations read as a system of ordinary differential equations. Such a method is well justified in the full plane, thanks to the explicit representation formulas of Biot and Savart. In an exterior domain, we also replace the impermeable boundary by a collection of point vortices generating the circulation...
Page 1