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The vortex method is a common numerical and theoretical approach used toimplement the motion of an ideal flow, in which the vorticity is approximatedby a sum of point vortices, so that the Euler equations read as a system ofordinary differential equations. Such a method is well justified in the fullplane, thanks to the explicit representation formulas of Biot and Savart. In anexterior domain, we also replace the impermeable boundary by a collection ofpoint vortices generating the circulation around the obstacle. The density ofthese point vortices is chosen in order that the flow remains tangent atmidpoints between adjacent vortices. In this work, we provide a rigorousjustification for this method in exterior domains. One of the main mathematicaldifficulties being that the Biot-Savart kernel defines a singular integraloperator when restricted to a curve. For simplicity and clarity, we only treatthe case of the unit disk in the plane approximated by a uniformly distributedmesh of point vortices. The complete and general version of our work isavailable in [arXiv:1707.01458].

The vortex method for 2D ideal flows in the exterior of a disk