Title: The vortex method for 2D ideal flows in the exterior of a disk,
Abstract: 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 around the obstacle. The density of
these point vortices is chosen in order that the flow remains tangent at
midpoints between adjacent vortices. In this work, we provide a rigorous
justification for this method in exterior domains. One of the main mathematical
difficulties being that the Biot-Savart kernel defines a singular integral
operator when restricted to a curve. For simplicity and clarity, we only treat
the case of the unit disk in the plane approximated by a uniformly distributed
mesh of point vortices. The complete and general version of our work is
available in [arXiv:1707.01458].